Proof of an extension of E. Sawyer’s conjecture about weighted mixed weak-type estimates

LI, KANGWEI; PÉREZ, CARLOS; OMBROSI, SHELDY

MATHEMATISCHE ANNALEN

SPRINGER

Año: 2018

0025-5831

We show that if v ∈ A∞ and u ∈ A1, then there is a constant c depending on the A1constant of u and the A∞ constant of v such thatT ( f v)v L1,∞(uv)≤ c f L1(uv),where T can be the Hardy-Littlewood maximal function or any Calderón-Zygmund operator. This result was conjectured in Cruz-Uribe et al. (Int Math Res Not 30:1849?1871, 2005) and constitutes the most singular case of some extensions of several problems proposed by Sawyer and Muckenhoupt and Wheeden. We also improve and extends several quantitative estimates.