Endpoint estimates for bilinear pseudodifferential operators with symbol in BS^m_{1,1}

TL;DR

This paper establishes endpoint estimates for bilinear pseudodifferential operators with symbols in the BS^m_{1,1} class, connecting them with BMO spaces and deriving Kato-Ponce type estimates.

Contribution

It provides new endpoint estimates for bilinear pseudodifferential operators with symbols in BS^m_{1,1}, extending the understanding of their boundedness properties.

Findings

Endpoint estimates involving BMO spaces.

Extension of Kato-Ponce type estimates.

Advancement in bilinear pseudodifferential operator theory.

Abstract

In this paper we establish some endpoint estimates for bilinearpseudodifferential operators with symbol in the class BS^m_{1,1}, involving the space of functions with local bounded mean oscillation bmo. As a consequence we also obtain an endpoint estimate of Kato-Ponce type.