## Extrapolation and optimal decompositions: with applications to analysis, Issues 1579-1580 |

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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 applications Banach pair Banach space bilinear extrapolation bounded operator Calderon Chapter characteristic function commutator theorems compensated compactness computation concave functions consider Cwikel's defined denote detail developed embedding theorems end point equivalent estimates Example exists a constant extrapolation spaces extrapolation theorem fact families of spaces family of interpolation functional calculus give given Hardy's inequality implies infimum integral interpolation functors interpolation spaces interpolation theory iteration Iwaniec Jacobians K/J inequalities let f 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 order logarithmic Sobolev ordered pair orientation preserving map proof of Theorem prove quasi-concave function real interpolation rearrangement inequalities reiteration theorems relationship representation result follows Sbordone Sobolev imbedding theorems Sobolev spaces Suppose Theorem 67 tion triangle inequality weighted norm