Boundedness of bilinear pseudo-differential operators of $S_{0,0}$-type in Wiener amalgam spaces and in Lebesgue spaces

TL;DR

This paper investigates the boundedness of bilinear pseudo-differential operators with symbols in the H"ormander class, extending previous results by considering broader symbol classes and analyzing their behavior in Wiener amalgam and Lebesgue spaces.

Contribution

It introduces new boundedness results for bilinear pseudo-differential operators with wider symbol classes in Wiener amalgam and Lebesgue spaces, improving existing estimates.

Findings

Extended boundedness results for broader symbol classes.

Improved estimates for bilinear pseudo-differential operators.

Analysis in Wiener amalgam spaces enhances understanding of operator behavior.

Abstract

We extend and improve the known results about the boundedness of the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^{m}_{0,0}(\mathbb{R}^n)$. We consider wider classes of symbols and improve estimates for the corresponding operators. A key idea is to consider the operators in Wiener amalgam spaces.