Singular integral operators on tent spaces

TL;DR

This paper develops a theory for singular integral operators with operator-valued kernels on tent spaces, extending boundedness results and introducing off-diagonal decay conditions to handle time-space decay.

Contribution

It introduces a new framework for analyzing singular integral operators with operator-valued kernels on tent spaces, expanding the scope of boundedness results.

Findings

Established boundedness of maximal regularity operators on tent spaces.

Developed off-diagonal decay conditions for operator-valued kernels.

Extended singular integral operator theory to include time-space decay measures.

Abstract

We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly appropriate condition on the kernel is time-space decay measured by off-diagonal estimates with various exponents.