Sharp Maximal function estimates for Multilinear pseudo-differential operators of type (0,0)

TL;DR

This paper establishes sharp maximal function estimates for multilinear pseudo-differential operators of type (0,0), addressing the case where symbols lack decay upon differentiation, and introduces a novel approach distinct from previous methods for ho=0.

Contribution

The paper provides new sharp maximal estimates for multilinear pseudo-differential operators of type (0,0), expanding the understanding beyond previous results for ho > 0.

Findings

Established sharp maximal function bounds for type (0,0) operators

Developed a new approach differing from earlier methods for ho=0

Extended previous results to a broader class of operators

Abstract

In this paper, we study sharp maximal function estimates for multilinear pseudo-differential operators. Our target is operators of type (0, 0) for which a differentiation does not make any decay of the associated symbol. Analogous results for operators of type (\rho, \rho), 0 < \rho < 1, appeared in an earlier work of the authors, but a different approach is given for \rho = 0