Convex body domination for the commutator of vector valued operators with multiple matrix-valued symbols

TL;DR

This paper develops convex body domination techniques for vector-valued commutators with matrix-valued symbols, establishing strong type estimates and exploring related BMO spaces.

Contribution

It introduces convex body domination results for generalized vector-valued commutators with matrix symbols, advancing the understanding of their boundedness properties.

Findings

Established convex body domination for certain vector-valued commutators.

Proved strong type estimates for these operators.

Analyzed the BMO spaces associated with the context.

Abstract

We provide convex body domination results for the generalized vector-valued commutator of those operators that admit specific forms of convex body domination themselves. We also prove some strong type estimates and other consequences of these results, and we study the BMO spaces that appear naturally in this context.