EMBEDDINGS AND BOUNDEDNESS OF MULTIFUNCTIONAL OPERATORS IN TUBE DOMAINS OVER SYMMETRIC CONES ON BERGMAN AND HILBERT- HARDY SPACES

Sami   Ali; Ahmed Sufyan Abakar; Belgiss. A. A Obaid; Salih Yousuf Mohamed; Shawgy Hussein

Sami Ali University of Al-Butana, Faculty of education, Department of Physical and Mathematics, Sudan
Ahmed Sufyan Abakar Ministry of education Sultante of Oman
Belgiss. A. A Obaid Sudan University of Science and Technology, College of Science, Department of Mathematics, Sudan
Salih Yousuf Mohamed Bakht Al-Ruda University, College of Science, Department of Mathematics, Sudan
Shawgy Hussein Sudan University of Science and Technology, College of Science, Department of Mathematics, Sudan

Keywords: Bergman Projection, Symmetric Cones, Hardy Spaces, Tube Domains, Euclidean space, Bergman space

Abstract

We show a general sufficient conditions, introduced by Milos Arsenovic and Romi F. Shamoyan[12] for the continuity of the Bergman projection in tube domains over symmetric cones using multifunctional operators embeddings with some sharp embedding relations between the generalized Hilbert-Hardy spaces and the mixed-norm Bergman spaces.

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