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 $X$.

scholarly journals Variable Exponent Spaces of Analytic Functions

2020 ◽  
Author(s):  
Gerardo A. Chacón ◽  
Gerardo R. Chacón
Keyword(s):  
Hardy Spaces ◽  
Measurable Function ◽  
Analytic Functions ◽  
Variable Exponent ◽  
Bergman Spaces ◽  
Lebesgue Spaces ◽  
Basic Properties ◽  
Variable Exponent Spaces ◽  
Real Functions ◽  
Spaces Of Analytic Functions

Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

scholarly journals Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions

2021 ◽  
Vol 280 (3) ◽  
pp. 108834
Author(s):  
Pascal Lefèvre ◽  
Daniel Li ◽  
Hervé Queffélec ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Singular Numbers ◽  
Spaces Of Analytic Functions
Sign in / Sign up

Export Citation Format

Share Document