On the $L^2$-boundedness of pseudo-differential operators and their commutators with symbols in $\alpha$-modulation spaces

TL;DR

This paper investigates the conditions under which pseudo-differential operators with symbols in lpha-modulation spaces are bounded on L^2, contributing to the understanding of their analytical properties.

Contribution

It establishes new criteria for L^2-boundedness of pseudo-differential operators with symbols in lpha-modulation spaces, expanding previous boundedness results.

Findings

Derived sufficient conditions for L^2-boundedness

Extended boundedness results to a broader class of symbols

Provided new insights into the role of lpha-modulation spaces

Abstract

In this paper, we consider the $L^2$-boundedness of pseudo-differential operators with symbols in $\alpha$-modulation spaces.