Title

Unions of Lebesgue spaces and A1 majorants

Authors

Greg Knese, Washington University in St. LouisFollow
John E. McCarthy, Washington University in St LouisFollow
Kabe Moen

Author's School

Arts & Sciences

Author's Department

Mathematics

Document Type

Article

Publication Date

2-2016

Originally Published In

Pacific Journal of Mathematics in Vol. 280 (2016), No. 2, 411–432, published by Mathematical Sciences Publishers. DOI: 10.2140/pjm.2016.280.411

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 ofLwp(ℝn)spaces withw∈Apis 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.

Comments

First published in Pacific Journal of Mathematics in Vol. 280 (2016), No. 2, 411–432, published by Mathematical Sciences Publishers. DOI: 10.2140/pjm.2016.280.411

ORCID

http://orcid.org/0000-0002-9484-2537 [Knese] http://orcid.org/0000-0003-0036-7606 [McCarthy]

Recommended Citation

Knese, Greg; McCarthy, John E.; and Moen, Kabe, "Unions of Lebesgue spaces and A1 majorants" (2016). Mathematics Faculty Publications. 28.
https://openscholarship.wustl.edu/math_facpubs/28