scholarly journals О новых точных теоремах разложения для многофункциональных пространств типа ВМОА в ограниченных псевдовыпуклых областях

2020 ◽  
pp. 102-113
Author(s):  
R.F. Shamoyan ◽  
E.B. Tomashevskaya
Keyword(s):  
Unit Ball ◽  
Atomic Decomposition ◽  
Pseudoconvex Domains ◽  
Type Space ◽  
Type Spaces ◽  
Equivalent Expressions

We provide new equivalent expressions in the unit ball and pseudoconvex domains for multifunctional analytic BMOA type space. We extend in various directions a known theorem of atomic decomposition of BMOA type spaces in the unit ball. Мы приводим новые эквивалентные выражения в единичных шаровых и псевдовыпуклых областях для многофункционального аналитического пространства типа BMOA. Мы расширяем в различных направлениях известную теорему атомарного разложения пространств типа BMOA в единичном шаре.

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.

scholarly journals On New Decomposition Theorems in some Analytic Function Spaces in Bounded Pseudoconvex Domains

2020 ◽  
pp. 503-514
Author(s):  
Romi F. Shamoyan ◽  
Elena B. Tomashevskaya
Keyword(s):  
Analytic Function ◽  
Unit Ball ◽  
Analytic Functions ◽  
Atomic Decomposition ◽  
Smooth Boundary ◽  
Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Decomposition Theorems ◽  
Analytic Function Spaces ◽  
Spaces Of Analytic Functions

We provide new sharp decomposition theorems for multifunctional Bergman spaces in the unit ball and bounded pseudoconvex domains with smooth boundary expanding known results from the unit ball. Namely we prove that mΠ j=1 jjfj jjXj ≍ jjf1 : : : fmjj Ap for various (Xj) spaces of analytic functions in bounded pseudoconvex domains with smooth boundary where f; fj ; j = 1; : : : ;m are analytic functions and where Ap ; 0 < p < 1; > �����1 is a Bergman space. This in particular also extend in various directions a known theorem on atomic decomposition of Bergman Ap spaces.

scholarly journals Essential Norm of Operators into Weighted-Type Spaces on the Unit Ball

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Pablo Galindo ◽  
Mikael Lindström ◽  
Stevo Stević
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Type Space ◽  
Type Spaces ◽  
Weighted Type ◽  
General Banach Space

The essential norm of any operator from a general Banach space of holomorphic functions on the unit ball inℂninto the little weighted-type space is calculated. Some applications of the formula are given.

scholarly journals New characterizations for differences of composition operators between weighted-type spaces in the unit ball

2021 ◽  
Vol 73 (8) ◽  
pp. 1129-1139
Author(s):  
C. Chen
Keyword(s):  
Unit Ball ◽  
Necessary Conditions ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Spaces Of Holomorphic Functions ◽  
Type Spaces ◽  
Sufficient And Necessary Conditions ◽  
Weighted Type ◽  
Equivalent Expressions

In this paper, we present some asymptotically equivalent expressions to the essential norm of differences of composition operators acting on weighted-type spaces of holomorphic functions in the unit ball of . Especially, the descriptions in terms of are described. From which the sufficient and necessary conditions of compactness follows immediately. Also, we characterize the boundedness of these operators.

scholarly journals Improving KKM Theory on General Metric Type Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Sehie Park
Keyword(s):  
Convex Space ◽  
Metric Spaces ◽  
Space Theory ◽  
Type Space ◽  
Generalized Metric ◽  
Abstract Convex Space ◽  
Type Spaces

Abstract A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

scholarly journals Hadamard gap series in weighted-type spaces on the unit ball

2017 ◽  
Vol 8 (2) ◽  
pp. 259-269 ◽  
Author(s):  
Bingyang Hu ◽  
Songxiao Li
Keyword(s):  
Unit Ball ◽  
Gap Series ◽  
Type Spaces ◽  
Weighted Type

scholarly journals Non-smooth atomic decomposition of variable 2-microlocal Besov-type and Triebel–Lizorkin-type spaces

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Helena F. Gonçalves
Keyword(s):  
Atomic Decomposition ◽  
Morrey Spaces ◽  
Maximal Functions ◽  
Variable Exponents ◽  
Atomic Decompositions ◽  
Local Means ◽  
Essential Tool ◽  
Pointwise Multipliers ◽  
Type Spaces

AbstractIn this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) , q ( · ) w , ϕ ( R n ) and $$F^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ F p ( · ) , q ( · ) w , ϕ ( R n ) . Of big importance in general, and an essential tool here, are the characterizations of the spaces via maximal functions and local means, that we also present. These spaces were recently introduced by Wu et al. and cover not only variable 2-microlocal Besov and Triebel–Lizorkin spaces $$B^{\varvec{w}}_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) , q ( · ) w ( R n ) and $$F^{\varvec{w}}_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ F p ( · ) , q ( · ) w ( R n ) , but also the more classical smoothness Morrey spaces $$B^{s, \tau }_{p,q}({\mathbb {R}}^n)$$ B p , q s , τ ( R n ) and $$F^{s,\tau }_{p,q}({\mathbb {R}}^n)$$ F p , q s , τ ( R n ) . Afterwards, we state a pointwise multipliers assertion for this scale.

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