Characterization of boundedness on Wiener amalgam spaces of multilinear Rihaczek distributions

TL;DR

This paper characterizes the boundedness of multilinear Rihaczek distributions and pseudodifferential operators on Wiener amalgam spaces, establishing sharp exponents and a self-improvement property with applications to modulation spaces.

Contribution

It provides new characterizations and sharp boundedness exponents for multilinear Rihaczek distributions and pseudodifferential operators on Wiener amalgam spaces, extending previous results.

Findings

Established several boundedness characterizations for multilinear Rihaczek distributions.

Proved a self-improvement property with independent significance.

Derived sharp exponents for boundedness in key cases.

Abstract

In this paper, we give several characterizations for the boundedness of multilinear Rihaczek distributions acting from Wiener amalgam spaces to modulation and Fourier modulation spaces. Moreover, we establish the crucial self-improvement property which has its independent significance. As applications, sharp exponents are established for the boundedness in several typical cases. Correspondingly, the boundedness of pseudodifferential operators on Wiener amalgam spaces with symbols in modulation and Fourier modulation spaces are also established. In some typical cases, we also give the sharp exponents for the boundedness of pseudodifferential operators, including the recapture and essential extensions of the main results in \cite[IMRN, (10):1860-1893, (2010)]{CorderoNicola2010IMRNI} and \cite[JFAA, 23(4):810-816, (2017)]{Cunanan2017JoFAaA}.