On the ranges of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2 \times L^2$

TL;DR

This paper characterizes the output ranges of bilinear pseudo-differential operators of a specific class on L^2 spaces, enhancing understanding of their boundedness and behavior in Besov spaces.

Contribution

It extends the boundedness results of these operators from L^2 x L^2 to L^1, within the framework of Besov spaces, for symbols in the bilinear Hörmander class.

Findings

Determined the ranges of bilinear pseudo-differential operators in Besov spaces.

Improved boundedness results from L^2 x L^2 to L^1.

Enhanced understanding of operator behavior in function space frameworks.

Abstract

In this paper, the ranges of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2 \times L^2$ are determined in the framework of Besov spaces. Our result improves the $L^2 \times L^2 \to L^1$ boundedness of those operators with symbols in the bilinear H\"ormander class $BS^m_{0,0}$.