New York Journal of Mathematics
Volume 24 (2018), 902-928


David Békollé, Jocelyn Gonessa, and Cyrille Nana

Bergman-Lorentz spaces on tube domains over symmetric cones

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Published: October 6, 2018.
Keywords: Tube domain over a symmetric cone, Lorentz spaces, Bergman spaces, Bergman projectors, Bergman-Lorentz spaces, real interpolation, (quasi-) Banach spaces.
Subject: 32A25, 32A36, 32M15, 46E30, 46B70.

We study Bergman-Lorentz spaces on tube domains over symmetric cones, i.e. spaces of holomorphic functions which belong to Lorentz spaces L(p,q). We establish boundedness and surjectivity of Bergman projectors from Lorentz spaces to the corresponding Bergman-Lorentz spaces and real interpolation between Bergman-Lorentz spaces. Finally we ask a question whose positive answer would enlarge the interval of parameters p in (1, ∞) such that the relevant Bergman projector is bounded on Lp for cones of rank r greater than or equal to 3.


The authors wish to express their gratitude to Aline Bonami, Jacques Faraut, Gustavo Garrigós and Chokri Yacoub for valuable discussions. They are indebted to Michael Cwikel for pointing out section 3 of [16], which provided the proof of Theorem 5.5. They also thank the referee for his (her) thorough reading of the manuscript and his (her) many useful suggestions.

Author information

David Békollé:
Department of Mathematics, Faculty of Science, University of Ngaoundéré, P.O. Box 454, Ngaoundéré, Cameroon.

Jocelyn Gonessa:
Université de Bangui, Faculté des Sciences, Département de mathématiques et Informatique, BP. 908, Bangui, République Centrafricaine.

Cyrille Nana:
Faculty of Science, Department of Mathematics, University of Buea, P.O. Box 63, Buea, Cameroon.