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Hardy Type Inequalities For Abstract Differential Operators
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Book Synopsis Hardy type inequalities for abstract differential operators by : Werner O. Amrein
Download or read book Hardy type inequalities for abstract differential operators written by Werner O. Amrein and published by . This book was released on 1987 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hardy Type Inequalities for Abstract Differential Operators by : Werner O. Amrein
Download or read book Hardy Type Inequalities for Abstract Differential Operators written by Werner O. Amrein and published by American Mathematical Soc.. This book was released on 1987 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with certain estimates on the asymptotic behaviour of the functions [italic]u defined on an interval (a, [infinity symbol]) with values in a Hilbert space [italic]H. More precisely, if [italic]L is a second order ordinary differential operator the coefficients of which are operators acting in [italic]H, we wish to obtain inequalities allowing one to get information about the behaviour of a function [italic]u in a neighborhood of infinity from the asymptotic behaviour of the function [italic]L[italic]u. These inequalities will be called Hardy type inequalities.
Book Synopsis Weighted Inequalities Of Hardy Type by : Alois Kufner
Download or read book Weighted Inequalities Of Hardy Type written by Alois Kufner and published by World Scientific Publishing Company. This book was released on 2003-04-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.
Book Synopsis Weighted Inequalities of Hardy Type by : Alois Kufner
Download or read book Weighted Inequalities of Hardy Type written by Alois Kufner and published by World Scientific. This book was released on 2003 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.
Book Synopsis Hardy-type Inequalities by : Bohumír Opic
Download or read book Hardy-type Inequalities written by Bohumír Opic and published by Longman Scientific and Technical. This book was released on 1990 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hardy Inequalities on Homogeneous Groups by : Michael Ruzhansky
Download or read book Hardy Inequalities on Homogeneous Groups written by Michael Ruzhansky and published by Springer. This book was released on 2019-07-02 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
Book Synopsis Differential and Integral Inequalities by : Dorin Andrica
Download or read book Differential and Integral Inequalities written by Dorin Andrica and published by Springer. This book was released on 2020-11-27 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.
Book Synopsis Inequalities for Differential Forms by : Ravi P. Agarwal
Download or read book Inequalities for Differential Forms written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2009-09-19 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.
Book Synopsis Hardy Type Inequalities on Time Scales by : Ravi P. Agarwal
Download or read book Hardy Type Inequalities on Time Scales written by Ravi P. Agarwal and published by Springer. This book was released on 2016-10-20 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc.In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and the classical ones. To the best of the authors’ knowledge this is the first book devoted to Hardy-typeinequalities and their extensions on time scales.
Book Synopsis Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations by : Lakshmikantham
Download or read book Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations written by Lakshmikantham and published by Academic Press. This book was released on 1969 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations
Book Synopsis Hardy Inequalities and Applications by : Nikolai Kutev
Download or read book Hardy Inequalities and Applications written by Nikolai Kutev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-10-24 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. We focus on the optimality of Hardy constant and on its attainability. Applications include: results about existence\nonexistence and controllability for parabolic equations with double singular potentials; estimates from below of the fi rst eigenvalue of p-Laplacian with Dirichlet boundary conditions.
Book Synopsis Differential and Integral Inequalities: Theory and Applications by : V. Lakshmikantham
Download or read book Differential and Integral Inequalities: Theory and Applications written by V. Lakshmikantham and published by Academic Press. This book was released on 1969 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applicationsof differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.
Book Synopsis Survey on Classical Inequalities by : Themistocles RASSIAS
Download or read book Survey on Classical Inequalities written by Themistocles RASSIAS and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected] DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: [email protected] Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.
Book Synopsis Differential and Integral Inequalities: Functional, partial, abstract, and complex differential equations by : V. Lakshmikantham
Download or read book Differential and Integral Inequalities: Functional, partial, abstract, and complex differential equations written by V. Lakshmikantham and published by . This book was released on 1969 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Analysis and Geometry of Hardy's Inequality by : Alexander A. Balinsky
Download or read book The Analysis and Geometry of Hardy's Inequality written by Alexander A. Balinsky and published by Springer. This book was released on 2015-10-20 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.
Download or read book Inequalities written by Everitt and published by CRC Press. This book was released on 1990-11-30 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of an international conference organized by the London Mathematical Society, held July 1987 at the U. of Birmingham, and dominated by the ghosts of Hardy, Littlewood and Polya, whose Inequalities (still the primary reference in the field) appeared in 1934. Thirteen essays summarize subse
Book Synopsis Hardy Inequalities on Homogeneous Groups by : Durvudkhan Suragan
Download or read book Hardy Inequalities on Homogeneous Groups written by Durvudkhan Suragan and published by . This book was released on 2020-10-08 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.