Harmonic analysis
著者
書誌事項
Harmonic analysis
（A comprehensive course in analysis, pt. 3）
American Mathematical Society, c2015
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.
Part 3 returns to the themes of Part 1 by discussing pointwise limits (going beyond the usual focus on the Hardy-Littlewood maximal function by including ergodic theorems and martingale convergence), harmonic functions and potential theory, frames and wavelets, $H^p$ spaces (including bounded mean oscillation (BMO)) and, in the final chapter, lots of inequalities, including Sobolev spaces, Calderon-Zygmund estimates, and hypercontractive semigroups.
目次
Preliminaries
Pointwise convergence almost everywhere
Harmonic and subharmonic functions
Bonus chapter: Phase space analysis $H^p$ spaces and boundary values of analytic functions on the unit disk
Bonus chapter: More inequalities
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
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