Litte Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball

2021 ◽  
Vol 93 (3) ◽  
Author(s):  
David Békollé ◽  
Hugues Olivier Defo ◽  
Edgar L. Tchoundja ◽  
Brett D. Wick
Keyword(s):  
Unit Ball ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Vector Valued

scholarly journals OPERATORS ON BERGMAN SPACES

2021 ◽  
Vol 56 (5) ◽  
pp. 399-403
Author(s):  
Kifah Y. Alhami
Keyword(s):  
Invariant Subspace ◽  
Bergman Space ◽  
Hardy Spaces ◽  
Complex Analysis ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Space Theory ◽  
Shift Operators ◽  
The Core ◽  
Vector Valued

Bergman space theory has been at the core of complex analysis research for many years. Indeed, Hardy spaces are related to Bergman spaces. The popularity of Bergman spaces increased when functional analysis emerged. Although many researchers investigated the Bergman space theory by mimicking the Hardy space theory, it appeared that, unlike their cousins, Bergman spaces were more complex in different aspects. The issue of invariant subspace constitutes one common problem in mathematics that is yet to be resolved. For Hardy spaces, each invariant subspace for shift operators features an elegant description. However, the method for formulating particular structures for the large invariant subspace of shift operators upon Bergman spaces is still unknown. This paper aims to characterize bounded Hankel operators involving a vector-valued Bergman space compared to other different vector value Bergman spaces.

scholarly journals Schatten-von Neumann properties of bilinear Hankel forms of higher weights

2006 ◽  
Vol 98 (2) ◽  
pp. 283
Author(s):  
Marcus Sundhäll
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Besov Spaces ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Von Neumann ◽  
Higher Weights ◽  
Vector Valued

Hankel forms of higher weights, on weighted Bergman spaces in the unit ball of $\mathsf{C}^d$, were introduced by Peetre. Each Hankel form corresponds to a vector-valued holomorphic function, called the symbol of the form. In this paper we characterize bounded, compact and Schatten-von Neumann $\mathcal{S}_p$ class ($2\leq p<\infty$) Hankel forms in terms of the membership of the symbols in certain Besov spaces.

scholarly journals Compact Hankel operators on weighted harmonic Bergman spaces

1997 ◽  
Vol 39 (1) ◽  
pp. 77-84 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Ball ◽  
Harmonic Functions ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Spaces ◽  
Harmonic Bergman Spaces

AbstractWe prove the compactness of certain Hankel operators on weighted Bergman spaces of harmonic functions on the unit ball in Rn.

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

New atomic decompositions for Bergman spaces on the unit ball

2017 ◽  
Vol 66 (1) ◽  
pp. 205-235 ◽  
Author(s):  
Jens G Christensen ◽  
Karlheinz Grochenig ◽  
Gestur Olafsson
Keyword(s):  
Unit Ball ◽  
Bergman Spaces ◽  
Atomic Decompositions

scholarly journals Weighted BMO and Hankel operators between Bergman spaces

2016 ◽  
Vol 65 (5) ◽  
pp. 1639-1673 ◽  
Author(s):  
Jordi Pau ◽  
Ruhan Zhao ◽  
Kehe Zhu
Keyword(s):  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bmo

A Characterization of Bergman Spaces on the Unit Ball of ℂn. II

2012 ◽  
Vol 55 (1) ◽  
pp. 146-152 ◽  
Author(s):  
Songxiao Li ◽  
Hasi Wulan ◽  
Kehe Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Double Integrals

AbstractIt has been shown that a holomorphic function f in the unit ball of ℂn belongs to the weighted Bergman space , p > n + 1 + α, if and only if the function | f(z) – f(w)|/|1 – 〈z, w〉| is in Lp( × , dvβ × dvβ), where β = (p + α – n – 1)/2 and dvβ(z) = (1 – |z|2)βdv(z). In this paper we consider the range 0 < p < n + 1 + α and show that in this case, f ∈ (i) if and only if the function | f(z) – f(w)|/|1 – hz, wi| is in Lp( × , dvα × dvα), (ii) if and only if the function | f(z)– f(w)|/|z–w| is in Lp( × , dvα × dvα). We think the revealed difference in the weights for the double integrals between the cases 0 < p < n + 1 + α and p > n + 1 + α is particularly interesting.

Sign in / Sign up

Export Citation Format

Share Document