scholarly journals Lebesgue mixed norm estimates for Bergman projectors: from tube domains over homogeneous cones to homogeneous Siegel domains of type II

2018 ◽  
Vol 374 (1-2) ◽  
pp. 395-427
Author(s):  
David Békollé ◽  
Jocelyn Gonessa ◽  
Cyrille Nana
Keyword(s):  
Mixed Norm ◽  
Type Ii ◽  
Norm Estimates ◽  
Siegel Domains ◽  
Homogeneous Cones ◽  
Tube 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.

Mixed-Norm Estimates for the k-Plane Transform

2012 ◽  
pp. 211-228
Author(s):  
Javier Duoandikoetxea ◽  
Virginia Naibo
Keyword(s):  
Mixed Norm ◽  
Norm 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
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