Weighted variation inequalities for differential operators and singular integrals in higher dimensions

TL;DR

This paper establishes weighted q-variation inequalities for differential and singular integral operators in higher dimensions, extending the theory to vector-valued cases and broadening the understanding of their boundedness properties.

Contribution

It introduces weighted q-variation inequalities for higher-dimensional differential and singular integral operators, including their vector-valued extensions, which is a novel advancement.

Findings

Proved weighted q-variation inequalities for differential operators

Extended inequalities to singular integral operators in higher dimensions

Provided vector-valued versions of the inequalities

Abstract

We prove weighted $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators in higher dimensions. The vector-valued extensions of these inequalities are also given.