Fourier integrals in classical analysis
by Sogge, Christopher D., (Christopher Donald)
This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid re…
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- Full title :Fourier integrals in classical analysis / Christopher D. Sogge, the Johns Hopkins University.
Summary
This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat-Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.
This advanced monograph is concerned with modern treatments of central problems in harmonic analysis.
Edition Statements
- Publication Date:©2017
- Edition:Second edition
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:©2017
The Physical Object
- Description:1 online resource (xiv, 334 pages)
Edition Identifiers
- ISBN:9781108234733, 1108234739, 9781316341186, 1316341186
- oclc:ocn986802874
- LC Classification:QA404
- Dewey Decimal:515/.723
Table of Contents
Background -- Stationary phase -- Non-homogeneous oscillatory integral operators -- Pseudo-differential operators -- The half-wave operator and functions of pseudo-differential operators -- Lp estimates of eigenfunctions -- Fourier integral operators -- Propagation of singularities and refined estimates -- Local smoothing of Fourier integral operators -- Kakeya-type maximal operators.
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