A New Characterization of the Muckenhoupt Ap Weights Through an Extension of the Lorentz-Shimogaki Theorem

Abstract

Given any quasi-Banach function space X over Rn it is defined an index αX that coincides with the upper Boyd index ᾱX when the space X is rearrangement-invariant. This new index is defined by means of the local maximal operator mλf . It is shown then that the Hardy-Littlewood maximal operator M is bounded on X if and only if αX < 1 providing an extension of… (More)

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