Sparse domination for the lattice Hardy-Littlewood maximal operator

TL;DR

This paper investigates how the lattice Hardy-Littlewood maximal operator can be controlled by sparse operators within Banach lattices, revealing that the domination depends on the lattice's q-convexity.

Contribution

It establishes a link between the domination of the maximal operator and the q-convexity property of Banach lattices, extending sparse domination theory.

Findings

Sparse domination characterized by q-convexity of Banach lattices

Determined admissible exponents for sparse operators

Extended sparse domination results to general Banach lattices

Abstract

We study the domination of the lattice Hardy--Littlewood maximal operator by sparse operators in the setting of general Banach lattices. We prove that the admissible exponents of the dominating sparse operator are determined by the $q$-convexity of the Banach lattice.