Atomic decomposition and interpolation via the complex method for mixed norm Bergman spaces on tube domains over symmetric cones

David Békollè, Jocelyn Gonessa, Cyrille Nana

Type: Article

Publication Date: 2019-05-06

Citations: 1

DOI: https://doi.org/10.2422/2036-2145.201703_018

Abstract

Starting from an adapted Whitney decomposition of tube domains in C n over irreducible symmetric cones of R n , we prove an atomic decomposition theorem in mixed norm weighted Bergman spaces on these domains.We also characterize the interpolation space via the complex method between two mixed norm weighted Bergman spaces.

Locations

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE - View
arXiv (Cornell University) - View - PDF

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Action	Title	Year	Authors
+	Analysis on Symmetric Cones	1994	Jacques Faraut Adam Korányi
+	Operator theory in function spaces	1991	Kehe Zhu
+	Introduction to Fourier Analysis on Euclidean Spaces.	1971	Elias M. Stein Guido Weiss
+	Representation theorems for holomorphic and harmonic functions in L[P]	1980	Ronald R. Coifman Richard Rochberg Mitchell Taibleson Guido Weiss
+	Notes on Wolff's Note on Interpolation Spaces	1984	Svante Janson Per G. Nilsson Jaak Peetre Misha Zafran
+	Littlewood–Paley decompositions related to symmetric cones and Bergman projections in tube domains	2004	David Békollè Aline Bonami Gustavo Garrigós Fulvio Ricci
+ PDF Chat	Complex interpolation between two weighted Bergman spaces on tubes over symmetric cones	2003	David Békollè Jocelyn Gonessa Cyrille Nana
+ PDF Chat	Besov spaces and the boundedness of weighted Bergman projections over symmetric tube domains	2005	Daniele Debertol
+	Boundary values of harmonic functions in mixed norm spaces and their atomic structure	1983	Fulvio Ricci Mitchell Taibleson
+	Some questions related to the Bergman projection in symmetric domains	2015	Aline Bonami Cyrille Nana