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Displaying similar documents to “A generalization of the Shimogaki theorem”

Indices and interpolation

Lech Maligranda

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CONTENTS0. Introduction.............................................................................51. Submultiplicative functions and indices...................................72. Indices of measurable functions...........................................123. Indices of Orlicz spaces........................................................194. Indices of rearrangement invariant spaces...........................255. Interpolation theorems for weak type operators....................296....

Capacitary Orlicz spaces, Calderón products and interpolation

Pilar Silvestre (2014)

Banach Center Publications

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These notes are devoted to the analysis on a capacity space, with capacities as substitutes of measures of the Orlicz function spaces. The goal is to study some aspects of the classical theory of Orlicz spaces for these spaces including the classical theory of interpolation.

Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded.

Diego Gallardo (1988)

Publicacions Matemàtiques

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Let M be the Hardy-Littlewood maximal operator defined by: Mf(x) = supx ∈ Q 1/|Q| ∫Q |f| dx, (f ∈ Lloc(Rn)), where the supreme is taken over all cubes Q containing x and |Q| is the Lebesgue measure of Q. In this paper we characterize the Orlicz spaces Lφ*, associated to N-functions φ, such that M is bounded in Lφ*....

Interpolation of operators when the extreme spaces are L ∞

Jesús Bastero, Francisco Ruiz (1993)

Studia Mathematica

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Under some assumptions on the pair ( A 0 , B 0 ) , we study equivalence between interpolation properties of linear operators and monotonicity conditions for a pair (Y,Z) of rearrangement invariant quasi-Banach spaces when the extreme spaces of the interpolation are L ∞ . Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.