Real Variable Methods In Harmonic Analysis
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Real Variable Methods In Harmonic Analysis
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Author : Alberto Torchinsky
language : en
Publisher: Elsevier
Release Date : 2016-06-03
Real Variable Methods In Harmonic Analysis written by Alberto Torchinsky and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.
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.
Harmonic Analysis
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 1993-08
Harmonic Analysis written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08 with Mathematics categories.
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.
Harmonic Analysis Pms 43 Volume 43
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2016-06-02
Harmonic Analysis Pms 43 Volume 43 written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-02 with Mathematics categories.
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.
Real Variable Methods In Fourier Analysis
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Author :
language : en
Publisher: Elsevier
Release Date : 1981-01-01
Real Variable Methods In Fourier Analysis written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.
Real Variable Methods in Fourier Analysis
Geometric Aspects Of Harmonic Analysis
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Author : Paolo Ciatti
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Geometric Aspects Of Harmonic Analysis written by Paolo Ciatti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
This volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables. The work is addressed to researchers in the field.
Beijing Lectures In Harmonic Analysis Am 112 Volume 112
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Beijing Lectures In Harmonic Analysis Am 112 Volume 112 written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
Based on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular integrals, real-variable methods, and applications to several complex variables and partial differential equations. The different lecture series are closely interrelated; each contains a substantial amount of background material, as well as new results not previously published. The contributors to the volume are R. R. Coifman and Yves Meyer, Robert Fcfferman, Carlos K. Kenig, Steven G. Krantz, Alexander Nagel, E. M. Stein, and Stephen Wainger.
Classical And Multilinear Harmonic Analysis
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Author : Camil Muscalu
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-31
Classical And Multilinear Harmonic Analysis written by Camil Muscalu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Mathematics categories.
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Real Variable Methods In Fourier Analysis
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Author : Miguel de Guzmán
language : en
Publisher: North Holland
Release Date : 1981-01
Real Variable Methods In Fourier Analysis written by Miguel de Guzmán and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01 with Electronic books categories.
Harmonic Analysis Method For Nonlinear Evolution Equations I
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Author : Baoxiang Wang
language : en
Publisher: World Scientific
Release Date : 2011
Harmonic Analysis Method For Nonlinear Evolution Equations I written by Baoxiang Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
1. Fourier multiplier, function space [symbol]. 1.1. Schwartz space, tempered distribution, Fourier transform. 1.2. Fourier multiplier on L[symbol]. 1.3. Dyadic decomposition, Besov and Triebel spaces. 1.4. Embeddings on X[symbol]. 1.5. Differential-difference norm on [symbol]. 1.6. Homogeneous space [symbol] 1.7. Bessel (Riesz) potential spaces [symbol]. 1.8. Fractional Gagliardo-Nirenberg inequalities -- 2. Navier-Stokes equation. 2.1. Introduction. 2.2. Time-space estimates for the heat semi-group. 2.3. Global well-posedness in L[symbol] of NS in 2D. 2.4. Well-posedness in L[symbol] of NS in higher dimensions. 2.5. Regularity of solutions for NS -- 3. Strichartz estimates for linear dispersive equations. 3.1. [symbol] estimates for the dispersive semi-group. 3.2. Strichartz inequalities : dual estimate techniques. 3.3. Strichartz estimates at endpoints -- 4. Local and global wellposedness for nonlinear dispersive equations. 4.1. Why is the Strichartz estimate useful. 4.2. Nonlinear mapping estimates in Besov spaces. 4.3. Critical and subcritical NLS in H[symbol]. 4.4. Global wellposedness of NLS in L[symbol] and H[symbol]. 4.5. Critical and subcritical NLKG in H[symbol]. 5. The low regularity theory for the nonlinear dispersive equations. 5.1. Bourgain space. 5.2. Local smoothing effect and maximal function estimates. 5.3. Bilinear estimates for KdV and local well-posedness. 5.4. Local well-posedness for KdV in H[symbol]. 5.5. I-method. 5.6. Schrodinger equation with derivative. 5.7. Some other dispersive equations -- 6. Frequency-uniform decomposition techniques. 6.1. Why does the frequency-uniform decomposition work. 6.2. Frequency-uniform decomposition, modulation spaces. 6.3. Inclusions between Besov and modulation spaces. 6.4. NLS and NLKG in modulation spaces. 6.5. Derivative nonlinear Schrodinger equations -- 7. Conservations, Morawetz' estimates of nonlinear Schrodinger equations. 7.1. Nother's theorem. 7.2. Invariance and conservation law. 7.3. Virial identity and Morawetz inequality. 7.4. Morawetz' interaction inequality. 7.5. Scattering results for NLS -- 8. Boltzmann equation without angular cutoff. 8.1. Models for collisions in kinetic theory. 8.2. Basic surgery tools for the Boltzmann operator. 8.3. Properties of Boltzmann collision operator without cutoff. 8.4 Regularity of solutions for spatially homogeneous case
Fourier Analysis
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Author : Javier Duoandikoetxea Zuazo
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-01-01
Fourier Analysis written by Javier Duoandikoetxea Zuazo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
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.