Boundedness of some multi-parameter fiber-wise multiplier operators

TL;DR

This paper establishes $L^p$ bounds for multi-parameter fiber-wise multipliers, including bi- and trilinear operators, extending results to the bi-parameter twisted paraproduct.

Contribution

It provides new $L^p$ estimates for multi-parameter fiber-wise multipliers, including the bi-parameter twisted paraproduct, advancing the understanding of such operators.

Findings

Proved $L^p$ estimates for multi-parameter bi- and trilinear operators

Extended results to the bi-parameter twisted paraproduct

Enhanced understanding of fiber-wise multiplier operators

Abstract

We prove $L^p$ estimates for various multi-parameter bi- and trilinear operators with symbols acting on fibers of the two-dimensional functions. In particular, this yields estimates for the general bi-parameter form of the twisted paraproduct studied in arXiv:1011.6140.