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Extrapolation and Optimal Decompositions

with Applications to Analysis

  • Authors
  • Mario Milman

Part of the Lecture Notes in Mathematics book series (LNM, volume 1580)

Table of contents

About this book

Introduction

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.

Keywords

Sobolev spaces calculus compactness compensated compactness differential equation extrapolation interpolation logarithm maximum partial differential equation partial differential equations

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073498
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58081-2
  • Online ISBN 978-3-540-48439-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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