Extrapolation and Optimal Decompositions: with Applications to Analysis

Mario Milman (auth.)3540580816, 9783540580812

This book develops a theory of extrapolation spaces with applications to classical and modern analysis. Extrapolation theory aims to provide a general framework to study limiting estimates in analysis. The book also considers the role that optimal decompositions play in limiting inequalities incl. commutator estimates. Most of the results presented are new or have not appeared in book form before. A special feature of the book are the applications to other areas of analysis. Among them Sobolev imbedding theorems in different contexts including logarithmic Sobolev inequalities are obtained, commutator estimates are connected to the theory of comp. compactness, a connection with maximal regularity for abstract parabolic equations is shown, sharp estimates for maximal operators in classical Fourier analysis are derived.

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Table of contents :
Introduction….Pages 1-5
Background on extrapolation theory….Pages 7-34
K/J inequalities and limiting embedding theorems….Pages 35-41
Calculations with the Δ method and applications….Pages 43-57
Bilinear extrapolation and a limiting case of a theorem by Cwikel….Pages 59-73
Extrapolation, reiteration, and applications….Pages 75-93
Estimates for commutators in real interpolation….Pages 95-126
Sobolev imbedding theorems and extrapolation of infinitely many operators….Pages 127-130
Some remarks on extrapolation spaces and abstract parabolic equations….Pages 131-137
Optimal decompositions, scales, and Nash-Moser iteration….Pages 139-147