Multiplication and Composition in Weighted Modulation Spaces

TL;DR

This paper investigates the conditions under which products of weighted modulation spaces exist, introducing two strategies to analyze norm inequalities and the boundedness of composition operators.

Contribution

It presents two novel approaches for studying multiplication in weighted modulation spaces, including a detailed analysis of associated norm inequalities and composition operator boundedness.

Findings

Established conditions for the existence of products in weighted modulation spaces

Developed two strategies for analyzing norm inequalities

Explored boundedness of composition operators in this context

Abstract

We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer look onto associated norm inequalities under restrictions in the Fourier image. This will give us the opportunity to treat the boundedness of composition operators.