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Hardy-Littlewood maximal operator on the associate space of a Banach function space
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Resumo(s)
Let ε(X, d, μ) be a Banach function space over a space of homogeneous type (X, d, μ). We show that if the Hardy-Littlewood maximal operator M is bounded on the space ε(X, d, μ), then its boundedness on the associate space ε'(X, d, μ) is equivalent to a certain condition A∞. This result extends a theorem by Andrei Lerner from the Euclidean setting of ℝn to the setting of spaces of homogeneous type.
Descrição
info:eu-repo/grantAgreement/FCT/5876/147204/PT This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matemática e Aplicações).
Palavras-chave
Associate space Banach function space Dyadic cubes Hardy-Littlewood maximal operator Space of homogeneous type Analysis Geometry and Topology