Harmonic Analysis: A Comprehensive Course in Analysis Part 3

About this book

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 $Hp$ spaces (including bounded mean oscillation (BMO)) and in the final chapter lots of inequalities including Sobolev spaces Calderon-Zygmund estimates and hypercontractive semigroups.