Extrapolation and Optimal Decompositions
with Applications to Analysis
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Beschreibung
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.
Autor*in
Mario Milman
Themen in »Extrapolation and Optimal Decompositions«
Sobolev spaces calculus compactness compensated compactness differential equation extrapolation interpolation logarithm maximum partial differential equation partial differential equations