Harmonic Analysis: A Comprehensive Course in Analysis, Part 3
About this Title
Publication Year: 2015; Volume 3
ISBNs: 978-1-4704-1102-2 (print); 978-1-4704-2761-0 (online)
A Comprehensive Course in Analysis by Poincaré 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.
Researchers (mathematicians and some applied mathematicians and physicists) using analysis, professors teaching analysis at the graduate level, graduate students who need any kind of analysis in their work.
Table of Contents
- Chapter 1. Preliminaries
- Chapter 2. Pointwise convergence almost everywhere
- Chapter 3. Harmonic and subharmonic functions
- Chapter 4. Bonus chapter: Phase space analysis
- Chapter 5. $H^p$ spaces and boundary values of analytic functions on the unit disk
- Chapter 6. Bonus chapter: More inequalities