Boundedness of smooth bilinear square functions and applications to some bilinear pseudo-differential operators

TL;DR

This paper proves the boundedness of bilinear smooth square functions and applies these results to establish boundedness of certain bilinear pseudo-differential operators with specific symbol classes.

Contribution

It introduces new boundedness results for bilinear smooth square functions and applies them to a subclass of bilinear pseudo-differential operators.

Findings

Boundedness of bilinear smooth square functions established.

Boundedness of bilinear pseudo-differential operators with symbols in a specific class proven.

Abstract

This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging to a subclass of $BS^0_{0,0}$.