scholarly journals On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Romi F. Shamoyan ◽  
Olivera R. Mihić
Keyword(s):  
Analytic Functions ◽  
Smooth Boundary ◽  
Pseudoconvex Domains ◽  
Sharp Estimates ◽  
First Results ◽  
Type Spaces ◽  
Spaces Of Analytic Functions

New sharp estimates of traces of Bergman type spaces of analytic functions in bounded strictly pseudoconvex domains are obtained. These are, as far as we know, the first results of this type which are valid for any bounded strictly pseudoconvex domains with smooth boundary.

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 Atomic decompositions in weighted Bergman spaces of analytic functions on strictly pseudoconvex domains

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2545-2563
Author(s):  
Milos Arsenovic
Keyword(s):  
Analytic Functions ◽  
Atomic Decomposition ◽  
Smooth Boundary ◽  
Bergman Spaces ◽  
Real Variable ◽  
Weighted Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Atomic Decompositions ◽  
Strictly Pseudoconvex Domain ◽  
Spaces Of Analytic Functions

We construct an atomic decomposition of the weighted Bergman spaces Ap?(D) (0 < p ? 1, ? > -1) of analytic functions on a bounded strictly pseudoconvex domain D in Cn with smooth boundary. The atoms used are atoms in the real-variable sense.

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.

Extreme Points in Spaces of Analytic Functions

1968 ◽  
Vol 20 ◽  
pp. 919-928 ◽  
Author(s):  
T. W. Gamelin ◽  
M. Voichick
Keyword(s):  
Riemann Surface ◽  
Betti Number ◽  
Analytic Functions ◽  
Smooth Boundary ◽  
Extreme Points ◽  
Closed Curves ◽  
Open Riemann Surface ◽  
Spaces Of Analytic Functions

Our aim in this paper is to obtain some theorems concerning spaces of analytic functions on a finite open Riemann surface R which extend known results for the disc △ = {|z| < 1}. Suppose that R has a smooth boundary bR consisting of t closed curves, and that the interior genus of R is s. The first Betti number of R is then r = 2s + t — 1.

scholarly journals Monomial basis in Korenblum type spaces of analytic functions

2018 ◽  
Vol 146 (12) ◽  
pp. 5269-5278 ◽  
Author(s):  
José Bonet ◽  
Wolfgang Lusky ◽  
Jari Taskinen
Keyword(s):  
Analytic Functions ◽  
Monomial Basis ◽  
Type Spaces ◽  
Spaces Of Analytic Functions

scholarly journals Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Alexey Karapetyants ◽  
Stefan Samko
Keyword(s):  
Analytic Functions ◽  
Fractional Derivatives ◽  
Mixed Norm ◽  
Mixed Norm Spaces ◽  
Hardy Type ◽  
Type Spaces ◽  
Generalized Fractional Derivatives ◽  
Definition Of ◽  
Derivatives Of ◽  
Spaces Of Analytic Functions

AbstractThe aim of the paper is twofold. First, we present a new general approach to the definition of a class of mixed norm spaces of analytic functions 𝓐

Sign in / Sign up

Export Citation Format

Share Document