Mixed weak type inequalities in euclidean spaces and in spaces of homogeneous type

TL;DR

This paper establishes new mixed weak type inequalities for operators in Euclidean spaces and spaces of homogeneous type, extending previous results and being the first of their kind in the latter setting.

Contribution

It introduces the first mixed weak type estimates in spaces of homogeneous type, generalizing earlier Euclidean results and expanding the scope of such inequalities.

Findings

Established mixed weak type inequalities in Euclidean spaces.

Extended inequalities to spaces of homogeneous type.

First such results in the setting of spaces of homogeneous type.

Abstract

In this paper we provide mixed weak type inequalities generalizing previous results in an earlier work by Caldarelli and the second author and also in the spirit of earlier results by Lorente, Martell, P\'erez and Riveros. One of the main novelties is that, besides obtaining estimates in the euclidean setting, results are provided as well in spaces of homogeneous type, being the first mixed weak type estimates that we are aware of in that setting.