Continuity of pseudodifferential operators with nonsmooth symbols on mixed-norm Lebesgue spaces

TL;DR

This paper proves the boundedness of pseudodifferential operators with nonsmooth symbols on mixed-norm Lebesgue spaces, advancing the understanding of their continuity in PDE analysis.

Contribution

It introduces new results on the boundedness of nonsmooth symbol pseudodifferential operators on mixed-norm Lebesgue spaces, using recent pseudodifferential calculus advances.

Findings

Boundedness of pseudodifferential operators with nonsmooth symbols established

Extension of pseudodifferential calculus to mixed-norm Lebesgue spaces

Supports PDE theory with new continuity results

Abstract

Mixed-norm Lebesgue spaces found their place in the study of some questions in the theory of partial differential equations, as can be seen from recent interest in the continuity of certain classes of pseudodifferential operators on these spaces. In this paper, we use some recent advances in the pseudodifferential calculus for nonsmooth symbols to prove the boundedness of pseudodifferential operators with such symbols on mixed-norm Lebesgue spaces.