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Extrapolation and Optimal Decompositions

with Applications to Analysis

  • Book
  • © 1994

Overview

Authors:
  1. Mario Milman
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1580)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Mario Milman
    Pages 1-5

  3. Background on extrapolation theory

    • Mario Milman
    Pages 7-34

  4. K/J inequalities and limiting embedding theorems

    • Mario Milman
    Pages 35-41

  5. Calculations with the Δ method and applications

    • Mario Milman
    Pages 43-57

  6. Bilinear extrapolation and a limiting case of a theorem by Cwikel

    • Mario Milman
    Pages 59-73

  7. Extrapolation, reiteration, and applications

    • Mario Milman
    Pages 75-93

  8. Estimates for commutators in real interpolation

    • Mario Milman
    Pages 95-126

  9. Sobolev imbedding theorems and extrapolation of infinitely many operators

    • Mario Milman
    Pages 127-130

  10. Some remarks on extrapolation spaces and abstract parabolic equations

    • Mario Milman
    Pages 131-137

  11. Optimal decompositions, scales, and Nash-Moser iteration

    • Mario Milman
    Pages 139-147

  12. Back Matter

    Pages 149-163
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Keywords

About this book

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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