scholarly journals Some Carleson measures for the Hilbert–Hardy space of tube domains over symmetric cones

2018 ◽  
Vol 5 (2) ◽  
pp. 585-610
Author(s):  
David Békollé ◽  
Benoît F. Sehba
Keyword(s):  
Hardy Space ◽  
Carleson Measures ◽  
Symmetric Cones ◽  
Tube Domains

Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Hideto Nakashima
Keyword(s):  
Sufficient Conditions ◽  
Rational Functions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Symmetric Cones ◽  
The Real ◽  
Tube Domains ◽  
Homogeneous Cone ◽  
Necessary And Sufficient ◽  
Relative Invariants

AbstractIn this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

Some questions related to the Bergman projection in symmetric domains

2015 ◽  
Vol 6 (4) ◽  
Author(s):  
Aline Bonami ◽  
Cyrille Nana
Keyword(s):  
Bergman Projection ◽  
Symmetric Cones ◽  
Tube Domains ◽  
Rank 2

AbstractThis 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

scholarly journals From Hankel Operators to Carleson Measures in a Quaternionic Variable

2017 ◽  
Vol 60 (3) ◽  
pp. 565-585 ◽  
Author(s):  
Nicola Arcozzi ◽  
Giulia Sarfatti
Keyword(s):  
Hardy Space ◽  
Hankel Operators ◽  
Carleson Measures ◽  
Regular Functions

AbstractWe introduce and study Hankel operators defined on the Hardy space of regular functions of a quaternionic variable. Theorems analogous to those of Nehari and Fefferman are proved.

scholarly journals Embedding relations and boundedness of the multifunctional operators in tube domains over symmetric cones

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 109-126 ◽  
Author(s):  
Milos Arsenovic ◽  
Romi Shamoyan
Keyword(s):  
Hardy Spaces ◽  
Bergman Spaces ◽  
Bergman Projection ◽  
Symmetric Cones ◽  
Mixed Norm ◽  
Sufficient Condition ◽  
General Sufficient Condition ◽  
Tube Domains

We obtain a new general sufficient condition for the continuity of the Bergman projection in tube domains over symmetric cones using multifunctional embeddings. We also obtain some sharp embedding relations between the generalized Hilbert-Hardy spaces and the mixed-norm Bergman spaces in this setting.

scholarly journals The Duren–Carleson Theorem in Tube Domains over Symmetric Cones

2016 ◽  
Vol 86 (4) ◽  
pp. 475-494 ◽  
Author(s):  
David Békollé ◽  
Benoit F. Sehba ◽  
Edgar L. Tchoundja
Keyword(s):  
Symmetric Cones ◽  
Tube Domains
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