Extrapolation and optimal decompositions: with applications to analysis / Mario Milman

Auteur: Milman, Mario (1950-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1580Langue: anglaisÉditeur: Berlin : Springer-Verlag, 1994 ISBN: 9783540580812 ISSN: 1617-9692Note: ... The author surveys in detail the basic constructions in extra-polation theory and their connections with interpolation theory. Among other results, he discusses reiteration of extrapolation spaces and bilinear extrapolation. Special attention is paid to the role played by optimal decompositions in various constructions. Applications are given to several questions in analysis, including extrapolation of inequalities related to Sobolev embedding theorems, end-point estimates for the maximal operator of partial sums of Fourier series, higher-order logarithmic Sobolev inequalities, commutator inequalities and abstract parabolic equations. (MathSciNet) Sujets MSC: 46M35 Functional analysis -- Methods of category theory in functional analysis -- Abstract interpolation of topological vector spaces
46E35 Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B20 Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.)
35R15 Partial differential equations -- Miscellaneous topics -- Partial differential equations on infinite-dimensional (e.g. function) spaces
58D25 Global analysis, analysis on manifolds -- Spaces and manifolds of mappings -- Equations in function spaces; evolution equations
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... The author surveys in detail the basic constructions in extra-polation theory and their connections with interpolation theory. Among other results, he discusses reiteration of extrapolation spaces and bilinear extrapolation. Special attention is paid to the role played by optimal decompositions in various constructions. Applications are given to several questions in analysis, including extrapolation of inequalities related to Sobolev embedding theorems, end-point estimates for the maximal operator of partial sums of Fourier series, higher-order logarithmic Sobolev inequalities, commutator inequalities and abstract parabolic equations. (MathSciNet)

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