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
We study two questions. When does a function belong to the union of Lebesgue spaces, and when does a function have anA1majorant? 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.
Knese, Greg; McCarthy, John E.; and Moen, Kabe, "Unions of Lebesgue spaces and A1 majorants" (2016). Mathematics Faculty Publications. 28.