Unions of Lebesgue spaces and A1 majorants

Greg Knese; John E. McCarthy; Kabe Moen

doi:10.2140/pjm.2016.280.411

Unions of Lebesgue spaces and A₁ majorants

Greg Knese, John E. McCarthy, Kabe Moen

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study two questions. When does a function belong to the union of Lebesgue spaces, and when does a function have an A₁ majorant? We provide a systematic study of these questions and show that they are fundamentally related. We show that the union of L^p_w (ℝⁿ) spaces with w ∈ A_p is equal to the union of all Banach function spaces for which the Hardy- Littlewood maximal function is bounded on the space itself and its associate space.

Original language	English
Pages (from-to)	411-432
Number of pages	22
Journal	Pacific Journal of Mathematics
Volume	280
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2016.280.411
State	Published - 2016

Keywords

A spaces
Hardy spaces
L spaces
Maximal functions
Weighted L spaces

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10.2140/pjm.2016.280.411

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Unions of Lebesgue spaces and A₁ majorants

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Keywords

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