scholarly journals Hankel Operators on the WeightedLP-Bergman Spaces with Exponential Type Weights

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Hong Rae Cho ◽  
Jeong Wan Seo
Keyword(s):  
Exponential Type ◽  
Hankel Operator ◽  
Bergman Spaces ◽  
Hankel Operators

We characterize the boundedness and compactness of the Hankel operator with conjugate analytic symbols on the weightedLP-Bergman spaces with exponential type weights.

scholarly journals Bergman spaces with exponential type weights

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hicham Arroussi
Keyword(s):  
Exponential Type ◽  
Atomic Decomposition ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Hankel Operators ◽  
Weighted Bergman Space ◽  
Kernel Estimates ◽  
General Weight ◽  
Necessary And Sufficient

AbstractFor $1\le p<\infty $ 1 ≤ p < ∞ , let $A^{p}_{\omega }$ A ω p be the weighted Bergman space associated with an exponential type weight ω satisfying $$ \int _{{\mathbb{D}}} \bigl\vert K_{z}(\xi ) \bigr\vert \omega (\xi )^{1/2} \,dA(\xi ) \le C \omega (z)^{-1/2}, \quad z\in {\mathbb{D}}, $$ ∫ D | K z ( ξ ) | ω ( ξ ) 1 / 2 d A ( ξ ) ≤ C ω ( z ) − 1 / 2 , z ∈ D , where $K_{z}$ K z is the reproducing kernel of $A^{2}_{\omega }$ A ω 2 . This condition allows us to obtain some interesting reproducing kernel estimates and more estimates on the solutions of the ∂̅-equation (Theorem 2.5) for more general weight $\omega _{*}$ ω ∗ . As an application, we prove the boundedness of the Bergman projection on $L^{p}_{\omega }$ L ω p , identify the dual space of $A^{p}_{\omega }$ A ω p , and establish an atomic decomposition for it. Further, we give necessary and sufficient conditions for the boundedness and compactness of some operators acting from $A^{p}_{\omega }$ A ω p into $A^{q}_{\omega }$ A ω q , $1\le p,q<\infty $ 1 ≤ p , q < ∞ , such as Toeplitz and (big) Hankel operators.

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

The effect of boundary geometry on Hankel operators belonging to the trace ideals of Bergman spaces

1997 ◽  
Vol 28 (2) ◽  
pp. 196-213 ◽  
Author(s):  
Steven G. Krantz ◽  
Song-Ying Li ◽  
Richard Rochberg
Keyword(s):  
Bergman Spaces ◽  
Hankel Operators ◽  
Boundary Geometry

Toeplitz and Hankel Operators on Bergman Spaces

2021 ◽  
pp. 51-57
Author(s):  
M. Bourass ◽  
O. El-Fallah ◽  
I. Marrhich ◽  
H. Naqos
Keyword(s):  
Bergman Spaces ◽  
Hankel Operators

Hankel Operators on Pseudoconvex Domains of Finite Type in ℂ2

1998 ◽  
Vol 50 (3) ◽  
pp. 658-672 ◽  
Author(s):  
Frédéric Symesak
Keyword(s):  
Hardy Space ◽  
Finite Type ◽  
Pseudoconvex Domain ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Sufficient Condition ◽  
Schatten Class ◽  
Strictly Pseudoconvex Domain

AbstractThe aimof this paper is to study small Hankel operators h on the Hardy space or on weighted Bergman spaces,where Ω is a finite type domain in ℂ2 or a strictly pseudoconvex domain in ℂn. We give a sufficient condition on the symbol ƒ so that h belongs to the Schatten class Sp, 1 ≤ p < +∞.

On commutativity of weighted Hankel operators and their spectra

2015 ◽  
Vol 18 (03) ◽  
pp. 1550017 ◽  
Author(s):  
Gopal Datt ◽  
Deepak Kumar Porwal
Keyword(s):  
Hankel Operator ◽  
Hankel Operators ◽  
Weyl’S Theorem

In this paper, we describe the conditions on which the nonzero weighted Hankel operators [Formula: see text] and [Formula: see text] on H2(β) induced by ϕ ∈ L∞(β) and ψ ∈ L∞(β) respectively commute, where β = {βn}n∈ℤ is a sequence of positive numbers with β0 = 1. Spectrum of the weighted Hankel operator [Formula: see text], when ϕ(z) = az-1 + bz-2, is computed and it is also shown that the Weyl's theorem holds for the compact weighted Hankel operators.

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