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Author : J. Musielak
Publisher : Springer
ISBN 13 : 3540386920
Total Pages : 227 pages
Book Rating : 4.5/5 (43 download)
Download or read book Orlicz Spaces and Modular Spaces written by J. Musielak and published by Springer. This book was released on 2006-11-14 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 : 9780387127064
Total Pages : pages
Book Rating : 4.1/5 (27 download)
Download or read book Orlicz spaces and modular spaces written by and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Petteri Harjulehto
Publisher : Springer
ISBN 13 : 303015100X
Total Pages : 169 pages
Book Rating : 4.0/5 (31 download)
Download or read book Orlicz Spaces and Generalized Orlicz Spaces written by Petteri Harjulehto and published by Springer. This book was released on 2019-05-07 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
Author : Mohamed A. Khamsi
Publisher : Birkhäuser
ISBN 13 : 3319140515
Total Pages : 245 pages
Book Rating : 4.3/5 (191 download)
Download or read book Fixed Point Theory in Modular Function Spaces written by Mohamed A. Khamsi and published by Birkhäuser. This book was released on 2015-03-24 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, Calderon-Lozanovskii spaces, and others. In most cases, particularly in applications to integral operators, approximation and fixed point results, modular type conditions are much more natural and can be more easily verified than their metric or norm counterparts. There are also important results that can be proved only using the apparatus of modular function spaces. The material is presented in a systematic and rigorous manner that allows readers to grasp the key ideas and to gain a working knowledge of the theory. Despite the fact that the work is largely self-contained, extensive bibliographic references are included, and open problems and further development directions are suggested when applicable. The monograph is targeted mainly at the mathematical research community but it is also accessible to graduate students interested in functional analysis and its applications. It could also serve as a text for an advanced course in fixed point theory of mappings acting in modular function spaces.
Author : Osvaldo Mendez
Publisher : CRC Press
ISBN 13 : 0429537573
Total Pages : 175 pages
Book Rating : 4.4/5 (295 download)
Download or read book Analysis on Function Spaces of Musielak-Orlicz Type written by Osvaldo Mendez and published by CRC Press. This book was released on 2019-01-21 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introduction to the theory of Musielak–Orlicz spaces, and introduces associated function spaces, extending up to the current research on the topic Musielak-Orlicz spaces came under renewed interest when applications to electrorheological hydrodynamics forced the particular case of the variable exponent Lebesgue spaces on to center stage. Since then, research efforts have typically been oriented towards carrying over the results of classical analysis into the framework of variable exponent function spaces. In recent years it has been suggested that many of the fundamental results in the realm of variable exponent Lebesgue spaces depend only on the intrinsic structure of the Musielak-Orlicz function, thus opening the door for a unified theory which encompasses that of Lebesgue function spaces with variable exponent. Features Gives a self-contained, concise account of the basic theory, in such a way that even early-stage graduate students will find it useful Contains numerous applications Facilitates the unified treatment of seemingly different theoretical and applied problems Includes a number of open problems in the area
Author : Lars Diening
Publisher : Springer
ISBN 13 : 3642183638
Total Pages : 509 pages
Book Rating : 4.6/5 (421 download)
Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer. This book was released on 2011-03-29 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Author : J. Lindenstrauss
Publisher : Springer Science & Business Media
ISBN 13 : 3662353474
Total Pages : 253 pages
Book Rating : 4.6/5 (623 download)
Download or read book Classical Banach Spaces II written by J. Lindenstrauss and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Iwona Chlebicka
Publisher : Springer Nature
ISBN 13 : 3030888568
Total Pages : 389 pages
Book Rating : 4.0/5 (38 download)
Download or read book Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces written by Iwona Chlebicka and published by Springer Nature. This book was released on 2021-11-01 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth. The common property of the many different kinds of equations considered is that the growth conditions of the highest order operators lead to a formulation of the equations in Musielak–Orlicz spaces. This high level of generality, understood as full anisotropy and inhomogeneity, requires new proof concepts and a generalization of the formalism, calling for an extended functional analytic framework. This theory is established in the first part of the book, which serves as an introduction to the subject, but is also an important ingredient of the whole story. The second part uses these theoretical tools for various types of PDEs, including abstract and parabolic equations but also PDEs arising from fluid and solid mechanics. For connoisseurs, there is a short chapter on homogenization of elliptic PDEs. The book will be of interest to researchers working in PDEs and in functional analysis.
Author : Vyacheslav Chistyakov
Publisher : Springer
ISBN 13 : 3319252836
Total Pages : 137 pages
Book Rating : 4.3/5 (192 download)
Download or read book Metric Modular Spaces written by Vyacheslav Chistyakov and published by Springer. This book was released on 2015-12-14 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existence of solutions to ordinary differential equations in Banach spaces with rapidly varying right-hand sides.
Author : Z. Ditzian
Publisher : Springer Science & Business Media
ISBN 13 : 1461247780
Total Pages : 233 pages
Book Rating : 4.4/5 (612 download)
Download or read book Moduli of Smoothness written by Z. Ditzian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the introduction and application of a new measure for smoothness offunctions. Though we have both previously published some articles in this direction, the results given here are new. Much of the work was done in the summer of 1984 in Edmonton when we consolidated earlier ideas and worked out most of the details of the text. It took another year and a half to improve and polish many of the theorems. We express our gratitude to Paul Nevai and Richard Varga for their encouragement. We thank NSERC of Canada for its valuable support. We also thank Christine Fischer and Laura Heiland for their careful typing of our manuscript. z. Ditzian V. Totik CONTENTS Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 PART I. THE MODULUS OF SMOOTHNESS Chapter 1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1. Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2. Discussion of Some Conditions on cp(x). . . . • . . . . . . . • . . • . . • • . 8 . . . • . 1.3. Examples of Various Step-Weight Functions cp(x) . . • . . • . . • . . • . . . 9 . . • Chapter 2. The K-Functional and the Modulus of Continuity ... . ... 10 2.1. The Equivalence Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . 2.2. The Upper Estimate, Kr.tp(f, tr)p ~ Mw;(f, t)p, Case I . . . . . . . . . . . . 12 . . . 2.3. The Upper Estimate of the K-Functional, The Other Cases. . . . . . . . . . 16 . 2.4. The Lower Estimate for the K-Functional. . . . . . . . . . . . . . . . . . . 20 . . . . . Chapter 3. K-Functionals and Moduli of Smoothness, Other Forms. 24 3.1. A Modified K-Functional . . . . . . . . . . . . . . . . . . . . . . . . . . 24 . . . . . . . . . . 3.2. Forward and Backward Differences. . . . . . . . . . . . . . . . . . . . . . 26 . . . . . . . 3.3. Main-Part Modulus of Smoothness. . . . . . . . . . . . . . . . . . . . . . 28 . . . . . . .
Author : David V. Cruz-Uribe
Publisher : Springer Science & Business Media
ISBN 13 : 3034805489
Total Pages : 316 pages
Book Rating : 4.0/5 (348 download)
Download or read book Variable Lebesgue Spaces written by David V. Cruz-Uribe and published by Springer Science & Business Media. This book was released on 2013-02-12 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.
Author : Peter Kosmol
Publisher : Walter de Gruyter
ISBN 13 : 3110250209
Total Pages : 405 pages
Book Rating : 4.1/5 (12 download)
Download or read book Optimization in Function Spaces with Stability Considerations in Orlicz Spaces written by Peter Kosmol and published by Walter de Gruyter. This book was released on 2011 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus
Author : M.M. Rao
Publisher : CRC Press
ISBN 13 : 9780203910863
Total Pages : 496 pages
Book Rating : 4.9/5 (18 download)
Download or read book Applications Of Orlicz Spaces written by M.M. Rao and published by CRC Press. This book was released on 2002-02-08 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents previously unpublished material on the fundumental pronciples and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes. Provides practical applications in statistics and probability.
Author : Yoshihiro Sawano
Publisher : CRC Press
ISBN 13 : 1000064077
Total Pages : 316 pages
Book Rating : 4.0/5 ( download)
Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-16 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding
Author : Osvaldo Mendez
Publisher : CRC Press
ISBN 13 : 0429524102
Total Pages : 262 pages
Book Rating : 4.4/5 (295 download)
Download or read book Analysis on Function Spaces of Musielak-Orlicz Type written by Osvaldo Mendez and published by CRC Press. This book was released on 2019-01-21 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introduction to the theory of Musielak–Orlicz spaces, and introduces associated function spaces, extending up to the current research on the topic Musielak-Orlicz spaces came under renewed interest when applications to electrorheological hydrodynamics forced the particular case of the variable exponent Lebesgue spaces on to center stage. Since then, research efforts have typically been oriented towards carrying over the results of classical analysis into the framework of variable exponent function spaces. In recent years it has been suggested that many of the fundamental results in the realm of variable exponent Lebesgue spaces depend only on the intrinsic structure of the Musielak-Orlicz function, thus opening the door for a unified theory which encompasses that of Lebesgue function spaces with variable exponent. Features Gives a self-contained, concise account of the basic theory, in such a way that even early-stage graduate students will find it useful Contains numerous applications Facilitates the unified treatment of seemingly different theoretical and applied problems Includes a number of open problems in the area
Author : Lars Diening
Publisher : Springer Science & Business Media
ISBN 13 : 364218362X
Total Pages : 516 pages
Book Rating : 4.6/5 (421 download)
Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer Science & Business Media. This book was released on 2011-03-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Author : S. G. Krein
Publisher : American Mathematical Soc.
ISBN 13 : 0821831763
Total Pages : 390 pages
Book Rating : 4.8/5 (218 download)
Download or read book Interpolation of Linear Operators written by S. G. Krein and published by American Mathematical Soc.. This book was released on 2002-10-21 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:
