 

David Békollé,
Jocelyn Gonessa,
and Cyrille Nana
BergmanLorentz 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, BergmanLorentz spaces, real interpolation, (quasi) Banach spaces. 
Subject: 
32A25, 32A36, 32M15, 46E30, 46B70. 


Abstract
We study BergmanLorentz 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 BergmanLorentz spaces and real interpolation between BergmanLorentz 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 L^{p} for cones of rank r greater than
or equal to 3.


Acknowledgements
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.
dbekolle@univndere.cm
Jocelyn Gonessa:
Université de Bangui, Faculté des Sciences, Département de
mathématiques et Informatique,
BP. 908, Bangui, République Centrafricaine.
gonessa.jocelyn@gmail.com
Cyrille Nana:
Faculty of Science, Department of Mathematics,
University of Buea, P.O. Box 63, Buea, Cameroon.
nana.cyrille@ubuea.cm

