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Some questions related to the Bergman projection in symmetric domains
-
Aline Bonami
and
Cyrille Nana
Published/Copyright:
July 16, 2015
Abstract
This is essentially a survey on tube domains over irreducible symmetric cones or their bounded realizations. It includes the fact that in rank 2 these inequalities have now been proved for the whole range of possible exponents p, due to recent work of Bourgain and Demeter. We also discuss Lp estimates with loss for the bounded domains and conclude with some remarks and questions related to Bloch functions.
Funding source: Niels Henrik Abel Board
This paper was partly written when the second author was visiting MAPMO at Orléans. It is part of a joint research program with Gustavo Garrigós and it benefited from many discussions with him.
Received: 2014-11-28
Revised: 2015-2-25
Accepted: 2015-3-2
Published Online: 2015-7-16
Published in Print: 2015-10-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- Some questions related to the Bergman projection in symmetric domains
- Some uncertainty principles for diamond Lie groups
- Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
- Topology on the unitary dual of completely solvable Lie groups
- Rayleigh theorem, projection of orbital measures and spline functions
Keywords for this article
Bloch functions;
Bergman spaces;
Bergman projection;
bounded symmetric domains
Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- Some questions related to the Bergman projection in symmetric domains
- Some uncertainty principles for diamond Lie groups
- Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
- Topology on the unitary dual of completely solvable Lie groups
- Rayleigh theorem, projection of orbital measures and spline functions
