Optimal weak type estimates for dyadic-like maximal operators

TL;DR

This paper establishes precise weak-type bounds for the dyadic maximal operator under combined L1, Lq, and Lorentz space restrictions, advancing understanding of its distributional behavior.

Contribution

It introduces sharp weak estimates for the dyadic maximal operator with combined L1, Lq, and Lorentz space constraints, refining previous bounds.

Findings

Sharp weak estimates for M extphi under combined restrictions

Improved bounds for distribution functions of dyadic maximal operators

Enhanced understanding of maximal operator behavior in non-atomic spaces

Abstract

We provide sharp weak estimates for the distribution function of M\phi when on \phi we impose L1, Lq and Lp,1 restrictions. Here M is the dyadic maximal operator associated to a tree T on a non-atomic probability measure space.