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Recent Developments In The Theory Of Lorentz Spaces And Weighted Inequalities
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Book Synopsis Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities by : María J. Carro
Download or read book Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities written by María J. Carro and published by American Mathematical Soc.. This book was released on 2007 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this work is to bring together two well known and, a priori, unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$. for this, the authors consider the boundedness of $M$ in the weighted Lorentz space $\Lambdap u(w)$. Two examples are historically relevant as a motivation: If $w=1$, this corresponds to the study of the boundedness of $M$ on $Lp(u)$, which was characterized by B. Muckenhoupt in 1972, and the solution is given by the so called $A p$ weights. The second case is when we take $u=1$. This is a more recent theory, and was completely solved by M.A. Arino and B. Muckenhoupt in 1991. It turns out that the boundedness of $M$ on $\Lambdap(w)$ can be seen to be equivalent to the boundedness of the Hardy operator $A$ restricted to decreasing functions of $Lp(w)$, since the nonincreasing rearrangement of $Mf$ is pointwise equivalent to $Af*$. The class of weights satisfying this boundedness is known as $B p$. Even though the $A p$ and $B p$ classes enjoy some similar features, they come from very different theories, and so are the techniques used on each case: Calderon-Zygmund decompositions and covering lemmas for $A p$, rearrangement invariant properties and positive integral operators for $B p$. This work aims to give a unified version of these two theories. Contrary to what one could expect, the solution is not given in terms of the limiting cases above considered (i.e., $u=1$ and $w=1$), but in a rather more complicated condition, which reflects the difficulty of estimating the distribution function of the Hardy-Littlewood maximal operator with respect to general measures.
Book Synopsis Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities by : María J. Carro
Download or read book Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities written by María J. Carro and published by American Mathematical Soc.. This book was released on 2007 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this work is to bring together two well known and, a priori, unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$. For this, the authors consider the boundedness of $M$ in the weighted Lorentz space $\Lambdap u(w)$. Two examples are historically relevant as a motivation: If $w=1$, this corresponds to the study of the boundedness of $M$ on $Lp(u)$, which was characterized by B. Muckenhoupt in 1972, and the solution is given by the so called $A p$ weights. The second case is when we take $u=1$. This is a more recent theory, and was completely solved by M.A. Arino and B. Muckenhoupt in 1991. It turns out that the boundedness of $M$ on $\Lambdap(w)$ can be seen to be equivalent to the boundedness of the Hardy operator $A$ restricted to decreasing functions of $Lp(w)$, since the nonincreasing rearrangement of $Mf$ is pointwise equivalent
Book Synopsis Classical and Multidimensional Lorentz Spaces by : René Erlin Castillo
Download or read book Classical and Multidimensional Lorentz Spaces written by René Erlin Castillo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-09-07 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is solely dedicated to the study of both the one variable as well as the multidimensional Lorentz spaces covering the theory of Lebesgue type spaces invariant by rearrangement. The authors provide proofs in full detail for most theorems. The self-contained text is valuable for advanced students and researchers.
Book Synopsis New Trends in Applied Harmonic Analysis by : Akram Aldroubi
Download or read book New Trends in Applied Harmonic Analysis written by Akram Aldroubi and published by Birkhäuser. This book was released on 2016-04-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.
Book Synopsis Advanced Courses of Mathematical Analysis IV by : F. Javier Perez-Fernandez
Download or read book Advanced Courses of Mathematical Analysis IV written by F. Javier Perez-Fernandez and published by World Scientific. This book was released on 2012 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Proceedings contains a collection of articles by front-line researchers in Mathematical Analysis, giving the reader a wide perspective of the current research in several areas like Functional Analysis, Complex Analysis and Measure Theory. The works are a fundamental source for current and future developments in these research fields. The articles and surveys have been collected as well as reference results scattered in the corresponding literature and thus, are highly useful to researchers.
Book Synopsis The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra by : Michael Kapovich
Download or read book The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra written by Michael Kapovich and published by American Mathematical Soc.. This book was released on 2008 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the Saturation Conjecture for $GL(\ell)$ as a consequence of their solution of the corresponding saturation problem for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.
Book Synopsis Integral Operators in Non-Standard Function Spaces by : Vakhtang Kokilashvili
Download or read book Integral Operators in Non-Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-12 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors’ long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book’s most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Book Synopsis The Interaction of Analysis and Geometry by : Victor I. Burenkov
Download or read book The Interaction of Analysis and Geometry written by Victor I. Burenkov and published by American Mathematical Soc.. This book was released on 2007 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004), this title includes topics such as geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion, and nonlinear potential theory."
Book Synopsis Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications by : Philippe Barbe
Download or read book Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications written by Philippe Barbe and published by American Mathematical Soc.. This book was released on 2009 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: "January 2009, volume 197, number 922 (Fourth of five numbers)."
Book Synopsis Classical Fourier Analysis by : Loukas Grafakos
Download or read book Classical Fourier Analysis written by Loukas Grafakos and published by Springer. This book was released on 2014-11-17 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.
Book Synopsis Extended Abstracts 2021/2022 by : Michael Ruzhansky
Download or read book Extended Abstracts 2021/2022 written by Michael Ruzhansky and published by Springer Nature. This book was released on with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Index Theory, Eta Forms, and Deligne Cohomology by : Ulrich Bunke
Download or read book Index Theory, Eta Forms, and Deligne Cohomology written by Ulrich Bunke and published by American Mathematical Soc.. This book was released on 2009-03-06 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper sets up a language to deal with Dirac operators on manifolds with corners of arbitrary codimension. In particular the author develops a precise theory of boundary reductions. The author introduces the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator. Given a Dirac operator on a manifold with boundary faces the author uses the tamings of its boundary reductions in order to turn the operator into a Fredholm operator. Its index is an obstruction against extending the taming from the boundary to the interior. In this way he develops an inductive procedure to associate Fredholm operators to Dirac operators on manifolds with corners and develops the associated obstruction theory.
Book Synopsis Hardy Spaces and Potential Theory on $C^1$ Domains in Riemannian Manifolds by : Martin Dindoš
Download or read book Hardy Spaces and Potential Theory on $C^1$ Domains in Riemannian Manifolds written by Martin Dindoš and published by American Mathematical Soc.. This book was released on 2008 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies Hardy spaces on C1 and Lipschitz domains in Riemannian manifolds. Hardy spaces, originally introduced in 1920 in complex analysis setting, are invaluable tool in harmonic analysis. For this reason these spaces have been studied extensively by many authors.
Book Synopsis Invariant Differential Operators for Quantum Symmetric Spaces by : Gail Letzter
Download or read book Invariant Differential Operators for Quantum Symmetric Spaces written by Gail Letzter and published by American Mathematical Soc.. This book was released on 2008 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.
Book Synopsis Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings by : Wolfgang Bertram
Download or read book Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings written by Wolfgang Bertram and published by American Mathematical Soc.. This book was released on 2008 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed, without any restriction on the dimension or on the characteristic. Two basic features distinguish the author's approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.
Book Synopsis Minimal Resolutions via Algebraic Discrete Morse Theory by : Michael Jöllenbeck
Download or read book Minimal Resolutions via Algebraic Discrete Morse Theory written by Michael Jöllenbeck and published by American Mathematical Soc.. This book was released on 2009 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: "January 2009, volume 197, number 923 (end of volume)."
Book Synopsis Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems by : Sergey Zelik
Download or read book Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems written by Sergey Zelik and published by American Mathematical Soc.. This book was released on 2009-03-06 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study semilinear parabolic systems on the full space ${\mathbb R}^n$ that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of Sinai-Bunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.
