Free Interpolation in the Spaces of Analytic Functions With Derivative of Order s From the Hardy Space

2005 ◽  
Vol 129 (4) ◽  
pp. 4022-4039 ◽  
Author(s):  
A. M. Kotochigov
Keyword(s):  
Hardy Space ◽  
Analytic Functions ◽  
Free Interpolation ◽  
Spaces Of Analytic Functions

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 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.

scholarly journals Integration Operators in Average Radial Integrability Spaces of Analytic Functions

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Tanausú Aguilar-Hernández ◽  
Manuel D. Contreras ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Analytic Functions ◽  
Spaces Of Analytic Functions
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