scholarly journals The Cesàro operator on Korenblum type spaces of analytic functions

2017 ◽  
Vol 69 (2) ◽  
pp. 263-281 ◽  
Author(s):  
Angela A. Albanese ◽  
José Bonet ◽  
Werner J. Ricker
Keyword(s):  
Analytic Functions ◽  
Cesàro Operator ◽  
Type Spaces ◽  
Cesaro Operator ◽  
Spaces Of Analytic Functions

scholarly journals The Cesàro Operator in Growth Banach Spaces of Analytic Functions

2016 ◽  
Vol 86 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Angela A. Albanese ◽  
José Bonet ◽  
Werner J. Ricker
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Cesàro Operator ◽  
Cesaro Operator ◽  
Spaces Of Analytic Functions

scholarly journals Extensions of the classical Cesaro operator on Hardy spaces

2011 ◽  
Vol 108 (2) ◽  
pp. 279 ◽  
Author(s):  
Guillermo P. Curbera ◽  
Werner J. Ricker
Keyword(s):  
Banach Space ◽  
Hardy Space ◽  
Banach Spaces ◽  
Hardy Spaces ◽  
Analytic Functions ◽  
Cesàro Operator ◽  
Cesaro Operator ◽  
Spaces Of Analytic Functions

For each $1\le p<\infty$, the classical Cesàro operator $\mathcal C$ from the Hardy space $H^p$ to itself has the property that there exist analytic functions $f\notin H^p$ with ${\mathcal C}(f)\in H^p$. This article deals with the identification and properties of the (Banach) space $[{\mathcal C}, H^p]$ consisting of all analytic functions that $\mathcal C$ maps into $H^p$. It is shown that $[{\mathcal C}, H^p]$ contains classical Banach spaces of analytic functions $X$, genuinely bigger that $H^p$, such that $\mathcal C$ has a continuous $H^p$-valued extension to $X$. An important feature is that $[{\mathcal C}, H^p]$ is the largest amongst all such spaces $X$.

scholarly journals Extended Cesáro operators between generalized Besov spaces and Bloch type spaces in the unit ball

2009 ◽  
Vol 7 (3) ◽  
pp. 209-223 ◽  
Author(s):  
Ze-Hua Zhou ◽  
Min Zhu
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Besov Spaces ◽  
Complex Space ◽  
Bloch Space ◽  
Sufficient Conditions ◽  
Cesàro Operator ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Cesaro Operator

Let 𝑔 be a holomorphic of the unit ballBin then-dimensional complex space, and denote byTgthe extended Cesáro operator with symbolg. Let 0 <p< +∞, −n− 1 <q< +∞,q> −1 and α > 0, starting with a brief introduction to well known results about Cesáro operator, we investigate the boundedness and compactness ofTgbetween generalized Besov spaceB(p, q)and 𝛼α- Bloch spaceℬαin the unit ball, and also present some necessary and sufficient conditions.

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 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 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.

Bounds for the Weighted Hardy-Cesàro Operator and its Commutator on Morrey-Herz Type Spaces

2016 ◽  
Vol 35 (4) ◽  
pp. 489-504 ◽  
Author(s):  
Nguyen Minh Chuong ◽  
Dao Van Duong ◽  
Ha Duy Hung
Keyword(s):  
Cesàro Operator ◽  
Type Spaces ◽  
Cesaro Operator
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