scholarly journals Cesáro type operators on spaces of analytic functions

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 85-97 ◽  
Author(s):  
S. Naik
Keyword(s):  
Hardy Space ◽  
Analytic Functions ◽  
Bloch Space ◽  
Bounded Operator ◽  
Parameter Family ◽  
Spaces Of Analytic Functions ◽  
Two Parameter

In this article, we consider a two parameter family of generalized Ces?ro operators P b,c , Re (b + 1) > Re c > 0, on classical spaces of analytic functions such as Hardy (H p ), BMOA and a- Bloch space (Ba). We Prove that P b,c, Re(b+1)>Re c > 0 is bounded on H p if and only if p ?(0, ?) and on Ba if and only if a ? (1, ?) and unbounded on H ?, BMOA and Ba, a ?(0, 1]. Also we prove that ?-Cesaro operators C? is a bounded operator from the Hardy space H p to the Bergmann space Ap for p ? (0, 1). Thus, we improve some well known results of the literature.

On Analytic Functions of Bergman BMO in the Ball

1999 ◽  
Vol 42 (1) ◽  
pp. 97-103 ◽  
Author(s):  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Composition Operator ◽  
Analytic Functions ◽  
Bloch Space ◽  
Bounded Mean Oscillation ◽  
Open Unit ◽  
Bergman Metric ◽  
Open Unit Ball ◽  
Mean Oscillation ◽  
Volume Measure

AbstractLet B = Bn be the open unit ball of Cn with volume measure v, U = B1 and B be the Bloch space on , 1 ≤ α < 1, is defined as the set of holomorphic f : B → C for whichif 0 < α < 1 and , the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic f : B → U for which the composition operator defined by , is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric.

scholarly journals The Bloch space and Besov spaces of analytic functions

1996 ◽  
Vol 54 (2) ◽  
pp. 211-219 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Besov Spaces ◽  
Analytic Functions ◽  
Elementary Proof ◽  
Bloch Space ◽  
Little Bloch Space ◽  
Spaces Of Analytic Functions

We shall give an elementary proof of a characterisation for the Bloch space due to Holland and Walsh, and obtain analogous characterisations for the little Bloch space and Besov spaces of analytic functions on the unit disk in the complex plane.

scholarly journals Interpolating sequence on certain Banach spaces of analytic functions

2002 ◽  
Vol 65 (2) ◽  
pp. 177-182 ◽  
Author(s):  
B. Yousefi
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Connected Domain ◽  
Analytic Functions ◽  
Reflexive Banach Space ◽  
Bounded Operator ◽  
Interpolating Sequence ◽  
Spaces Of Analytic Functions

Let G be a finitely connected domain and let X be a reflexive Banach space of functions analytic on G which admits the multiplication Mz as a polynomially bounded operator. We give some conditions that a sequence in G has an interpolating subsequence for X.

scholarly journals Marcinkiewicz–Zygmund Inequalities for Polynomials in Bergman and Hardy Spaces

2021 ◽  
Author(s):  
Karlheinz Gröchenig ◽  
Joaquim Ortega-Cerdà
Keyword(s):  
Hardy Space ◽  
Bergman Space ◽  
Hilbert Spaces ◽  
Hardy Spaces ◽  
Analytic Functions ◽  
Infinite Dimensional ◽  
Bergman And Hardy Spaces ◽  
Sampling Sequences ◽  
The Relationship ◽  
Spaces Of Analytic Functions

AbstractWe study the relationship between sampling sequences in infinite dimensional Hilbert spaces of analytic functions and Marcinkiewicz–Zygmund inequalities in subspaces of polynomials. We focus on the study of the Hardy space and the Bergman space in one variable because they provide two settings with a strikingly different behavior.

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 $X$.

Linear Isometries of some Normed Spaces of Analytic Functions

1985 ◽  
Vol 37 (1) ◽  
pp. 62-74 ◽  
Author(s):  
W. P. Novinger ◽  
D. M. Oberlin
Keyword(s):  
Hardy Space ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Normed Spaces ◽  
Space Of Analytic Functions ◽  
Image Position ◽  
Spaces Of Analytic Functions ◽  
Linear Isometries

For 1 ≦ p < ∞ let Hp denote the familiar Hardy space of analytic functions on the open unit disc D and let ‖·‖ denote the Hp norm. Let Sp denote the space of analytic functions f on D such that f′ ∊ Hp. In this paper we will describe the linear isometries of Sp into itself when Sp is equipped with either of two norms. The first norm we consider is given by(1)and the second by(2)(It is well known [1, Theorem 3.11] that f′ ∊ Hp implies continuity for f on D, the closure of D. Thus (2) actually defines a norm on Sp.) In the former case, with the norm defined by (1), we will show that an isometry of Sp induces, in a sense to be made precise in Section 2, an isometry of Hp and that Forelli's characterization [2] of the isometries of Hp can thus be used to describe the isometries of Hp.

scholarly journals UNBOUNDED HERMITIAN OPERATORS ON KOLASKI SPACES

2013 ◽  
Vol 56 (3) ◽  
pp. 507-517
Author(s):  
JAMES JAMISON ◽  
RAENA KING
Keyword(s):  
Analytic Functions ◽  
Bloch Space ◽  
Hermitian Operator ◽  
Normed Spaces ◽  
Compact Resolvent ◽  
Analytical Functions ◽  
Groups Of Isometries ◽  
Spaces Of Analytic Functions

AbstractWe investigate strongly continuous one-parameter (C0) groups of isometries acting on certain spaces of analytical functions which were introduced by Kolaski (C. J. Kolaski, Isometries of some smooth normed spaces of analytic functions, Complex Var. Theory Appl. 10(2–3) (1988), 115–122). We characterize the generators of these groups of isometries and also the spectrum of the generators. We provide an example on the Bloch space of an unbounded hermitian operator with non-compact resolvent.

scholarly journals Norms of inclusions between some spaces of analytic functions

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Adrián Llinares
Keyword(s):  
Besov Spaces ◽  
Analytic Functions ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Spaces Of Analytic Functions

AbstractThe inclusions between the Besov spaces $$B^q$$ B q , the Bloch space $$\mathcal {B}$$ B and the standard weighted Bergman spaces $$A^p_{\alpha}$$ A α p are completely understood, but the norms of the corresponding inclusion operators are in general unknown. In this work, we compute or estimate asymptotically the norms of these inclusions.

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