The Cauchy Transform of Continuous Linear Functionals and Projections on the Weighted Spaces of Analytic Functions

2005 ◽  
Vol 46 (6) ◽  
pp. 969-994 ◽  
Author(s):  
O. E. Antonenkova ◽  
F. A. Shamoyan
Keyword(s):  
Analytic Functions ◽  
Weighted Spaces ◽  
Cauchy Transform ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Spaces Of Analytic Functions

scholarly journals On M-ideals and o-O type spaces

2017 ◽  
Vol 121 (1) ◽  
pp. 151 ◽  
Author(s):  
Karl-Mikael Perfekt
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Function Spaces ◽  
Weighted Spaces ◽  
Bounded Mean Oscillation ◽  
Mean Oscillation ◽  
Type Spaces ◽  
Invariant Spaces ◽  
Holder Spaces ◽  
Spaces Of Analytic Functions

We consider pairs of Banach spaces $(M_0, M)$ such that $M_0$ is defined in terms of a little-$o$ condition, and $M$ is defined by the corresponding big-$O$ condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, Möbius invariant spaces of analytic functions, Lipschitz-Hölder spaces, etc. It has previously been shown that the bidual $M_0^{**}$ of $M_0$ is isometrically isomorphic with $M$. The main result of this paper is that $M_0$ is an M-ideal in $M$. This has several useful consequences: $M_0$ has Pełczýnskis properties (u) and (V), $M_0$ is proximinal in $M$, and $M_0^*$ is a strongly unique predual of $M$, while $M_0$ itself never is a strongly unique predual.

scholarly journals Whitney Decomposition, Embedding Theorems and Interpolation Questions in Weighted Spaces of Analytic Functions

2019 ◽  
Author(s):  
Ф.А. Шамоян ◽  
Е.В. Тасоева
Keyword(s):  
Analytic Functions ◽  
Weighted Spaces ◽  
Embedding Theorems ◽  
Whitney Decomposition ◽  
Spaces Of Analytic Functions

По классической теореме Уитни каждое открытое множество на плоскости можно представить в виде объединения специальных квадратов, внутренности которых не пересекаются. В статье, используя эти свойства квадратов Уитни, вводится новое понятие: для каждого центра $a_k$ квадрата Уитни существует точка $a_k^*\in C/G$ такая, что расстояние до границы открытого множества $G$ заключается между двумя константами независимо от $k$. Используя свойства Уитни в~статье, в частности, устанавливается необходимое и достаточное условие на ${z_k }_1^{\infty}\subset G$, при котором оператор $R(f)=(f(z_1),f(z_2),\ldots,f(z_n),\ldots)$ отображает обобщенные плоские классы Неванлинны по множеству $G$ в $l^p.$

H(ϕ) Spaces

1986 ◽  
Vol 29 (3) ◽  
pp. 295-301 ◽  
Author(s):  
W. Deeb ◽  
M. Marzuq
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Almost Everywhere ◽  
Subadditive Function

AbstractLet ψ be a non-decreasing continuous subadditive function defined on [0, ∞) and satisfy ψ(x) = 0 if and only if x = 0. The space H(ψ) is defined as the set of analytic functions in the unit disk which satisfyand the space H+ (ψ) is the space of a f ∊ H(ψ) for whichwhere almost everywhere.In this paper we study the H(ψ) spaces and characterize the continuous linear functionals on H+ (ψ).

Complemented Submodules in Weighted Spaces of Analytic Functions

1992 ◽  
Vol 157 (1) ◽  
pp. 263-276 ◽  
Author(s):  
Michael Langenbruch ◽  
Siegfried Momm
Keyword(s):  
Analytic Functions ◽  
Weighted Spaces ◽  
Spaces Of Analytic Functions
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