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 О КЛАССАХ ТИПА ХАРДИ В НЕКОТОРЫХ ОБЛАСТЯХ В Cn И СВЯЗАННЫЕ С НИМИ ПРОБЛЕМЫ

2019 ◽  
pp. 12-37
Author(s):  
R.F. Shamoyan ◽  
V.V. Loseva
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Bergman Spaces ◽  
Poisson Integral ◽  
Pseudoconvex Domains ◽  
Mixed Norm ◽  
Convex Domains ◽  
Hardy Type ◽  
Type Spaces ◽  
Decomposition Theorems

We discuss some new problems in several new mixed norm Hardy type spaces in products of bounded pseudoconvex domains with smooth boundary in Cnand then prove some new sharp decomposition theorems for multifunctional Hardy type spaces in the unit ball and then we show also similar results in pseudoconvex and convex domains of finite type extending previously known assertions obtained by first author earlier in Bergman spaces under certain Poisson integral type condition which vanishes in one functional case. Some new (in particular sharp in the unit ball) embeddings for some new mixed norm Hardy spaces in bounded pseudoconvex domains will be also indicated. Some new extensions of Poisson integral in the unit ball and some new assertions concerning them will be indicated and discussed in product domains. Some related multifunctional results are also given.Some new embedding theorems are also provided in some new mixed norm Hardy spaces in unbounded tubular domains over symmetric cones. Введены несколько новых шкал пространств типа Харди со смешанной нормой в единичном шаре, в ограниченных псевдовыпуклых областях и в трубчатых областях над симметрическими конусами в Cn. В этих пространствах обобщающих известное пространство Харди обсуждаются различные задачи. Для пространств такого типа в единичном шаре приводятся в частности точные многофункциональные теоремы вложения типа Карлесона, приводятся также некоторые многофункциональные максимальные теоремы. В трубчатых и в псевдовыпуклых областях получены некоторые прямые аналоги и частичные обобщения этих теорем вложения. При одном дополнительном интегральном условии получены теоремы декомпозиции для весовых мультифункциональных пространств Харди в областях указанного типа,обобщающие ранее известные теоремы такого рода в случае обычных однофункциональных весовых пространств Харди. Ранее первым автором теоремы такого типа были получены в многофункциональных пространствах Бергмана. Наконец вводится прямое обобще ние интеграла типа Пуассона в произведении единичных шаров в Cnи обсуждаются некоторые задачи и обобщения известных результатов связанные с ним.

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 On Bergman-type spaces in tubular domains over symmetric cones

2020 ◽  
pp. 22-29
Author(s):  
Romi Shamoyan
Keyword(s):  
Bergman Spaces ◽  
Integral Operators ◽  
Integral Condition ◽  
Symmetric Cones ◽  
Type Integral ◽  
Tube Domains ◽  
Type Spaces ◽  
Atomic Type ◽  
Type Decomposition

Some properties of new Bergman-type integral operators on product of the tube domains are obtained. An integral condition in tube to get atomic-type decomposition in multifunctional analytic Bergman spaces in tube domains over symmetric cones are provided.

Fourier transform of anisotropic mixed-norm Hardy spaces

2021 ◽  
Vol 16 (1) ◽  
pp. 119-139
Author(s):  
Long Huang ◽  
Der-Chen Chang ◽  
Dachun Yang
Keyword(s):  
Fourier Transform ◽  
Hardy Spaces ◽  
Mixed Norm

A Combinatorial Distinction Between Unit Circles and Straight Lines: How Many Coincidences Can they Have?

2009 ◽  
Vol 18 (5) ◽  
pp. 691-705 ◽  
Author(s):  
GYÖRGY ELEKES ◽  
MIKLÓS SIMONOVITS ◽  
ENDRE SZABÓ
Keyword(s):  
Parameter Family ◽  
Sufficient Condition ◽  
Simple Application ◽  
Quadratic Number ◽  
General Sufficient Condition ◽  
Family Of Curves ◽  
Unit Circles ◽  
Triple Points ◽  
Straight Lines ◽  
Special Case

We give a very general sufficient condition for a one-parameter family of curves not to have n members with ‘too many’ (i.e., a near-quadratic number of) triple points of intersections. As a special case, a combinatorial distinction between straight lines and unit circles will be shown. (Actually, this is more than just a simple application; originally this motivated our results.)

scholarly journals Hardy spaces and analytic continuation of Bergman spaces

1998 ◽  
Vol 126 (3) ◽  
pp. 435-482 ◽  
Author(s):  
Wolfgang Bertram ◽  
Joachim Hilgert
Keyword(s):  
Analytic Continuation ◽  
Hardy Spaces ◽  
Bergman Spaces
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