The Dual of the Bergman Space A 1 in Symmetric Siegel Domains of Type II

1986 ◽  
Vol 296 (2) ◽  
pp. 607 ◽  
Author(s):  
David Bekolle
Keyword(s):  
Bergman Space ◽  
Type Ii ◽  
Siegel Domains

KORÁNYI’S LEMMA FOR HOMOGENEOUS SIEGEL DOMAINS OF TYPE II. APPLICATIONS AND EXTENDED RESULTS

2014 ◽  
Vol 90 (1) ◽  
pp. 77-89 ◽  
Author(s):  
DAVID BÉKOLLÉ ◽  
HIDEYUKI ISHI ◽  
CYRILLE NANA
Keyword(s):  
Functional Analysis ◽  
Bergman Kernel ◽  
Atomic Decomposition ◽  
Bergman Spaces ◽  
Decomposition Theorem ◽  
Interpolation Theorem ◽  
Type Ii ◽  
Siegel Domain ◽  
Homogeneous Case ◽  
Siegel Domains

AbstractWe show that the modulus of the Bergman kernel $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}B(z, \zeta )$ of a general homogeneous Siegel domain of type II is ‘almost constant’ uniformly with respect to $z$ when $\zeta $ varies inside a Bergman ball. The control is expressed in terms of the Bergman distance. This result was proved by A. Korányi for symmetric Siegel domains of type II. Subsequently, R. R. Coifman and R. Rochberg used it to establish an atomic decomposition theorem and an interpolation theorem by functions in Bergman spaces $A^p$ on these domains. The atomic decomposition theorem and the interpolation theorem are extended here to the general homogeneous case using the same tools. We further extend the range of exponents $p$ via functional analysis using recent estimates.

scholarly journals Hua System and Pluriharmonicity for Symmetric Irreducible Siegel Domains of Type II

2002 ◽  
Vol 188 (1) ◽  
pp. 38-74 ◽  
Author(s):  
Aline Bonami ◽  
Dariusz Buraczewski ◽  
Ewa Damek ◽  
Andrzej Hulanicki ◽  
Richard Penney ◽  
...  
Keyword(s):  
Type Ii ◽  
Siegel Domains

scholarly journals Classification of homogeneous bounded domains of lower dimension

1974 ◽  
Vol 53 ◽  
pp. 1-46 ◽  
Author(s):  
Soji Kaneyuki ◽  
Tadashi Tsuji
Keyword(s):  
The Other ◽  
Type I ◽  
Bounded Domains ◽  
Type Ii ◽  
Large Classes ◽  
Siegel Domains ◽  
Dual Cones ◽  
Definition Of ◽  
Lower Dimensional

The theory of classification of homogeneous bounded domains in the complex number space Cn has been developed mainly in the recent papers [10], [6], [3] and [7]. As a result, the classification is reduced to that of S-algebras due to Takeuchi [7] which correspond to irreducible Siegel domains of type I or type II (For the definition of irreducibility see § 1). On the other hand Pjateckii-Sapiro [5] found large classes of homogeneous Siegel domains obtained from classical self-dual cones. Even in lower-dimensional cases, however, there are still homogeneous Siegel domains which do not appear in his results.

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