The maximal regularity operator on tent spaces

TL;DR

This paper develops weighted maximal regularity estimates in tent spaces for a range of p values, extending the theory for non-smooth boundary value problems with L^2 data and exploring the case p=∞.

Contribution

It introduces new weighted maximal regularity estimates in tent spaces, advancing the L^p theory for boundary value problems with non-smooth data.

Findings

Established weighted maximal regularity estimates in tent spaces T^{p,2} for p in an open range.

Extended the theory to include the case p=∞.

Provided foundational results for non-smooth boundary value problems.

Abstract

Recently, Auscher and Axelsson gave a new approach to non-smooth boundary value problems with $L^{2}$ data, that relies on some appropriate weighted maximal regularity estimates. As part of the development of the corresponding $L^{p}$ theory, we prove here the relevant weighted maximal estimates in tent spaces $T^{p,2}$ for $p$ in a certain open range. We also study the case $p=\infty$.