Kato-Ponce type inequality for bilinear pseudo-differential operators of $S_{0,0}$-type in the scale of Besov spaces

TL;DR

This paper investigates the boundedness of bilinear pseudo-differential operators with $S_{0,0}$-type symbols within Besov spaces, focusing on the critical borderline cases for their boundedness.

Contribution

It provides new insights into the Kato-Ponce type inequality for these operators, especially addressing the borderline cases of boundedness in Besov spaces.

Findings

Boundedness of bilinear pseudo-differential operators analyzed

Borderline cases of boundedness discussed

Conditions for boundedness in Besov spaces established

Abstract

We consider the Kato-Ponce type inequality for bilinear pseudo-differential operators with $S_{0,0}$-type symbols in the scale of Besov spaces. In particular, the borderline whether the boundedness of those operators holds or not is discussed.