Dimension-free estimates for the vector-valued variational operators

TL;DR

This paper establishes dimension-free $L^p$ bounds for vector-valued variational operators related to Hardy-Littlewood averages over Euclidean balls, advancing understanding of their behavior in high-dimensional spaces.

Contribution

It provides the first dimension-free $L^p$ estimates for UMD lattice-valued $q$-variations of these averaging operators.

Findings

Proves dimension-free bounds for vector-valued variational operators

Extends results to UMD lattice-valued functions

Enhances understanding of high-dimensional harmonic analysis

Abstract

In this paper, We study dimension-free $L^p$ estimates for UMD lattice-valued $q$-variations of Hardy-Littlewood averaging operators associated with the Euclidean balls.