Embedding relations and boundedness of the multifunctional operators in tube domains over symmetric cones

TL;DR

This paper establishes new conditions for the continuity of the Bergman projection in tube domains over symmetric cones and explores embedding relations between generalized Hilbert-Hardy and mixed norm Bergman spaces.

Contribution

It provides a novel sufficient condition for Bergman projection continuity and sharp embedding relations in symmetric cone tube domains.

Findings

New sufficient condition for Bergman projection continuity

Sharp embedding relations between Hilbert-Hardy and Bergman spaces

Enhanced understanding of multifunctional embeddings in symmetric cones

Abstract

We obtain a new general sufficient condition for the continuity of the Bergman projection in tube domains over symmetric cones using multifunctional embeddings.We also obtain some sharp embedding relations between the generalized Hilbert-HArdy spaces and the mixed norm Bergman spaces in this setting.