Harmonic Analysis: A Comprehensive Course in Analysis, Part 3

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.

• Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A
• Advanced Complex Analysis: A Comprehensive Course in Analysis, Part 2B
• Operator Theory: A Comprehensive Course in Analysis, Part 4
• Real Analysis: A Comprehensive Course in Analysis, Part 1
• Partial Differential Equations: Second Edition (Graduate Studies in Mathematics)
• Partial Differential Equations III: Nonlinear Equations (Applied Mathematical Sciences)
• Partial Differential Equations II: Qualitative Studies of Linear Equations (Applied Mathematical Sciences)
• Partial Differential Equations I: Basic Theory (Applied Mathematical Sciences)