On Schatten-von Neumann class properties of pseudo-differential operators. The Cordes-Kato method

TL;DR

This paper studies the Schatten-class properties of pseudo-differential operators using a revisited Cordes-Kato method, focusing on symbol classes with $L^{p}$-conditions instead of $L^{}$-conditions.

Contribution

It extends the Cordes-Kato method to analyze pseudo-differential operators with $L^{p}$-symbol classes, broadening the understanding of their Schatten-class properties.

Findings

Established Schatten-class criteria for pseudo-differential operators with $L^{p}$-symbol classes.

Generalized previous results by replacing $L^{}$-conditions with $L^{p}$-conditions.

Provided new insights into the spectral properties of these operators.

Abstract

We investigate the Schatten-class properties of pseudo-differential operators with the (revisted) method of Cordes and Kato. As symbol classes we use classes similar to those of Cordes in which the $L^{\infty}$% -conditions are replaced by $L^{p}$-conditions, $1\leq p<\infty $.