On Hermite pseudo-multipliers

TL;DR

This paper extends a theorem on $L^p$ boundedness of operators, providing new kernel conditions for weighted estimates and establishing $L^p$ boundedness of Hermite pseudo-multipliers.

Contribution

It introduces sufficient kernel conditions for weighted $L^p$ estimates and applies them to prove boundedness of Hermite pseudo-multipliers.

Findings

Established kernel conditions imply weighted $L^p$ bounds.

Proved $L^p$ boundedness of Hermite pseudo-multipliers.

Extended Mauceri's theorem to new operator classes.

Abstract

In this article we deal with a variation of a theorem of Mauceri concerning the $ L^p $ boundedness of operators $ M $ which are known to be bounded on $ L^2.$ We obtain sufficient conditions on the kernel of the operaor $ M $ so that it satisfies weighted $ L^p $ estimates. As an application we prove $ L^p $ boundedness of Hermite pseudo-multipliers.