Characterization of Some Properties on Weighted Modulation Spaces

TL;DR

This paper investigates properties of weighted modulation and Wiener amalgam spaces by relating them to weighted Lebesgue spaces, providing sharp conditions for inequalities and embeddings that extend existing results.

Contribution

It introduces new characterizations of properties on weighted modulation and Wiener amalgam spaces based on weighted Lebesgue spaces, improving and extending prior results.

Findings

Sharp conditions for product inequalities established

Convolution inequalities characterized precisely

Embedding relations between spaces clarified

Abstract

In this paper, some properties on weighted modulation and Wiener amalgam spaces are characterized by the corresponding properties on weighted Lebesgue spaces. As applications, sharp conditions for product inequalities, convolution inequalities and embedding on weighted modulation and Wiener amalgam spaces are obtained. These applications improve and extend many known results.