Contractive inequalities for mixed norm spaces and the Beta function

TL;DR

This paper characterizes when contractive inequalities hold between pairs of mixed norm spaces, including weighted Bergman spaces, with implications for Number Theory and Mathematical Physics.

Contribution

It provides a comprehensive characterization of contractive inequalities for mixed norm spaces, extending to weighted Bergman spaces and related applications.

Findings

Identifies all pairs of mixed norm spaces with contractive inequalities

Includes new results for weighted Bergman spaces

Connects inequalities to applications in Number Theory and Physics

Abstract

For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many pairs of weighted Bergman spaces. Some inequalities of this type are motivated by their applications in Number Theory and in Mathematical Physics.