Harmonic Analysis: Part 3
āĻ¨ā§ąā§ ā§¨ā§Ļā§§ā§Ģ ¡ A comprehensive course in analysis āĻāĻŋāĻ¤āĻžāĻĒ 3 ¡ American Mathematical Soc.
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A Comprehensive Course in Analysis by PoincarÊ 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, Â Â Â spaces (including bounded mean oscillation (BMO)) and, in the final chapter, lots of inequalities, including Sobolev spaces, Calderon-Zygmund estimates, and hypercontractive semigroups.
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Barry Simon, California Institute of Technology, Pasadena, CA
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