Trace ideals for pseudo-differential operators and their commutators with symbols in $\alpha$-modulation spaces

TL;DR

This paper investigates the trace properties of pseudo-differential operators whose symbols belong to lpha-modulation spaces, aiming to understand their mathematical structure and potential applications.

Contribution

It introduces new results on the trace class criteria for pseudo-differential operators with lpha-modulation space symbols, expanding the theoretical framework.

Findings

Established trace class conditions for these operators

Characterized commutators with symbols in lpha-modulation spaces

Extended previous results to a broader class of symbols

Abstract

In this paper, we consider the trace property of pseudo-differential operators with symbols in $\alpha$-modulation spaces.