Real-variable Methods in Harmonic Analysis
Author | : |
Publisher | : Academic Press |
Total Pages | : 475 |
Release | : 1986-11-06 |
Genre | : Mathematics |
ISBN | : 0080874428 |
Real-variable Methods in Harmonic Analysis
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Author | : |
Publisher | : Academic Press |
Total Pages | : 475 |
Release | : 1986-11-06 |
Genre | : Mathematics |
ISBN | : 0080874428 |
Real-variable Methods in Harmonic Analysis
Author | : Elias M. Stein |
Publisher | : Princeton University Press |
Total Pages | : 712 |
Release | : 2016-06-02 |
Genre | : Mathematics |
ISBN | : 140088392X |
This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.
Author | : Alberto Torchinsky |
Publisher | : Elsevier |
Total Pages | : 475 |
Release | : 2016-06-03 |
Genre | : Mathematics |
ISBN | : 1483268888 |
Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.
Author | : Camil Muscalu |
Publisher | : Cambridge University Press |
Total Pages | : 389 |
Release | : 2013-01-31 |
Genre | : Mathematics |
ISBN | : 0521882451 |
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Author | : Camil Muscalu |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2013-01-31 |
Genre | : Mathematics |
ISBN | : 1107031826 |
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Author | : Alexey N. Karapetyants |
Publisher | : Springer Nature |
Total Pages | : 585 |
Release | : 2021-09-27 |
Genre | : Mathematics |
ISBN | : 3030774937 |
This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.
Author | : Baoxiang Wang |
Publisher | : World Scientific |
Total Pages | : 298 |
Release | : 2011-08-10 |
Genre | : Mathematics |
ISBN | : 9814458392 |
This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.
Author | : Elias M. Stein |
Publisher | : Princeton University Press |
Total Pages | : 710 |
Release | : 1993-08 |
Genre | : Mathematics |
ISBN | : 0691032165 |
This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.
Author | : Anton Deitmar |
Publisher | : Springer Science & Business Media |
Total Pages | : 154 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 147573834X |
This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
Author | : Javier Duoandikoetxea Zuazo |
Publisher | : American Mathematical Soc. |
Total Pages | : 248 |
Release | : 2001-01-01 |
Genre | : Mathematics |
ISBN | : 9780821883846 |
Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autonoma de Madrid and incorporates lecture notes from a course taught by José Luis Rubio de Francia at the same university. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities, H1, BMO spaces, and the T1 theorem, are discussed. Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform in higher dimensions. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between H1, BMO, and singular integrals; Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the T1 theorem, which has been of crucial importance in the field. This volume has been updated and translated from the original Spanish edition (1995). Minor changes have been made to the core of the book; however, the sections, "Notes and Further Results" have been considerably expanded and incorporate new topics, results, and references. It is geared toward graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis.