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Author : Yongsheng Han,Eric T. Sawyer
Publisher : Unknown
Page : 126 pages
File Size : 50,9 Mb
Release : 1994
Category : Function spaces
ISBN : 1470401096
Author : Yongsheng Han,Eric T. Sawyer
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 41,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825921
In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calder 'on reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.
Author : Michael Frazier,Björn Jawerth,Guido Weiss
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 50,7 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821807316
Littlewood-Paley theory was developed to study function spaces in harmonic analysis and partial differential equations. Recently, it has contributed to the development of the *q-transform and wavelet decompositions. Based on lectures presented at the NSF-CBMS Regional Research Conference on Harmonic Analysis and Function Spaces, held at Auburn University in July 1989, this book is aimed at mathematicians, as well as mathematically literate scientists and engineers interested in harmonic analysis or wavelets. The authors provide not only a general understanding of the area of harmonic analysis relating to Littlewood-Paley theory and atomic and wavelet decompositions, but also some motivation and background helpful in understanding the recent theory of wavelets. The book begins with some simple examples which provide an overview of the classical Littlewood-Paley theory. The *q-transform, wavelet, and smooth atomic expansions are presented as natural extensions of the classical theory. Finally, applications to harmonic analysis (Calderon-Zygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.
Author : Ioseb Genebashvili,Amiran Gogatishvili,Vakhtang Kokilashvil,Miroslav Krbec
Publisher : CRC Press
Page : 432 pages
File Size : 52,7 Mb
Release : 1997-05-15
Category : Mathematics
ISBN : 0582302951
This volume gives an account of the current state of weight theory for integral operators, such as maximal functions, Riesz potential, singular integrals and their generalization in Lorentz and Orlicz spaces. Starting with the crucial concept of a space of homogeneous type, it continues with general criteria for the boundedness of the integral operators considered, then address special settings and applications to classical operators in Euclidean spaces.
Author : Steve Hofmann,Dorina Mitrea,Marius Mitrea
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 43,7 Mb
Release : 2017-01-18
Category : Function spaces
ISBN : 9781470422608
The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.
Author : Marcin Bownik
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 54,5 Mb
Release : 2003
Category : Hardy spaces
ISBN : 9780821833261
Investigates the anisotropic Hardy spaces associated with very general discrete groups of dilations. This book includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky.
Author : Hans Triebel
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 49,6 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9783764375829
This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.
Author : Minde Cheng,Dong-gao Deng,Sheng Gong,Chung-Chun Yang
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401101417
Harmonic Analysis in China is a collection of surveys and research papers written by distinguished Chinese mathematicians from within the People's Republic of China and expatriates. The book covers topics in analytic function spaces of several complex variables, integral transforms, harmonic analysis on classical Lie groups and manifolds, LP- estimates of the Cauchy-Riemann equations and wavelet transforms. The reader will also be able to trace the great influence of the late Professor Loo-keng Hua's ideas and methods on research into harmonic analysis on classical domains and the theory of functions of several complex variables. Western scientists will thus become acquainted with the unique features and future trends of harmonic analysis in China. Audience: Analysts, as well as engineers and physicists who use harmonic analysis.
Author : Brian Street
Publisher : Walter de Gruyter GmbH & Co KG
Page : 768 pages
File Size : 44,5 Mb
Release : 2023-07-03
Category : Mathematics
ISBN : 9783111085647
Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.
Author : Nigel Kalton,Elias Saab,Stephen Montgomery-Smith
Publisher : CRC Press
Page : 496 pages
File Size : 47,6 Mb
Release : 1995-10-12
Category : Mathematics
ISBN : 082479611X
Based on a conference on the interaction between functional analysis, harmonic analysis and probability theory, this work offers discussions of each distinct field, and integrates points common to each. It examines developments in Fourier analysis, interpolation theory, Banach space theory, probability, probability in Banach spaces, and more.
Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 938 pages
File Size : 51,9 Mb
Release : 2023-03-03
Category : Mathematics
ISBN : 9783031137181
This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. Volume II is concerned with function spaces measuring size and/or smoothness, such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, etc., in general geometric settings. Work here also highlights the close interplay between differentiability properties of functions and singular integral operators. The text is intended for researchers, graduate students, and industry professionals interested in harmonic analysis, functional analysis, geometric measure theory, and function space theory.
Author : Genaro López Acedo,Rafael Villa Caro
Publisher : Universidad de Sevilla
Page : 322 pages
File Size : 55,5 Mb
Release : 2004
Category : Mathematical analysis
ISBN : 8447208575
This volume consists of the lecture notes of the Seminar on Mathematical Analysis which was held at the Universities of Malaga and Seville, Septembre 2002-February 2003.
Author : Hans Triebel
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 50,7 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034805698
This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations. The book is self-contained, although some parts may be considered as a continuation of the author's book Fractals and Spectra. It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated. - - - The book under review can be regarded as a continuation of [his book on "Fractals and spectra", 1997] (...) There are many sections named: comments, preparations, motivations, discussions and so on. These parts of the book seem to be very interesting and valuable. They help the reader to deal with the main course. (Mathematical Reviews)
Author : Donggao Deng,Yongsheng Han
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 45,7 Mb
Release : 2008-11-19
Category : Mathematics
ISBN : 9783540887447
This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ̈ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.
Author : Hans Plesner Jakobsen
Publisher : American Mathematical Soc.
Page : 129 pages
File Size : 43,5 Mb
Release : 1994
Category : Hilbert space
ISBN : 9780821825938
This work contains a complete description of the set of all unitarizable highest weight modules of classical Lie superalgebras. Unitarity is defined in the superalgebraic sense, and all the algebras are over the complex numbers. Part of the classification determines which real forms, defined by anti-linear anti-involutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.
