## Extrapolation and optimal decompositions: with applications to analysisThis 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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### Contents

Introduction | 1 |

Background On Extrapolation Theory | 7 |

KJ Inequalities and Limiting Embedding Theorems | 35 |

Copyright | |

8 other sections not shown

### Common terms and phrases

absolute constant analysis applications Banach pair Banach space bilinear extrapolation bounded operator Calderon Chapter characteristic function commutator theorems compensated compactness computation concave functions consider corresponding Cwikel defined denote detailed developed embedding theorems end point equivalent estimates Example exists a constant extrapolation spaces extrapolation theorem fact families of spaces family of interpolation functional calculus given Hardy's inequality implies infimum interpolation functors interpolation spaces interpolation theory Iwaniec Jacobians K/J inequalities linear operator LLogL log+ logarithmic Sobolev inequalities Lp spaces Macaev ideals measurable functions method of interpolation min(l min{l moreover mutually closed pair Nash-Moser theorem notation obtain optimal decompositions ordered pair orientation preserving map proof of Theorem prove quasi-concave function real interpolation rearrangement inequalities reiteration theorems relationship representation result follows Sbordone semigroup Sobolev imbedding theorems Sobolev spaces strongly compatible Suppose Theorem 67 tion triangle inequality