Boundedness of multilinear pseudo-differential operators with symbols in the H\"ormander class $S_{0,0}$

TL;DR

This paper characterizes when multilinear pseudo-differential operators with symbols in the H"ormander class $S_{0,0}$ are bounded on local Hardy spaces and Wiener amalgam spaces, extending bilinear results.

Contribution

It provides a complete characterization of boundedness for these operators on Hardy and Wiener amalgam spaces, improving upon previous bilinear results.

Findings

Operators are bounded on local Hardy spaces under specific conditions.

Results extend known bilinear boundedness to multilinear cases.

Includes new boundedness results for Wiener amalgam spaces.

Abstract

The multilinear pseudo-differential operators with symbols in the multilinear H\"ormander class $S_{0,0}$ are considered. A complete identification of the cases where those operators define bounded operators between local Hardy spaces is given. Some results for the boundedness between Wiener amalgam spaces are also given. These are extensions and improvements of the results known in the bilinear case.