scholarly journals Interpolating sequences for weighted Bergman spaces on strongly pseudoconvex bounded domains

2021 ◽  
pp. 2150026
Author(s):  
Hamzeh Keshavarzi
Keyword(s):  
Unit Ball ◽  
Bounded Domain ◽  
Interpolation Problem ◽  
Smooth Boundary ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Bounded Domains ◽  
Interpolating Sequences ◽  
Conjugate Exponent

Let [Formula: see text], [Formula: see text], and [Formula: see text] be a strongly pseudoconvex bounded domain with a smooth boundary in [Formula: see text]. We will study the interpolation problem for weighted Bergman spaces [Formula: see text]. In the case, [Formula: see text], and [Formula: see text], where [Formula: see text] is the conjugate exponent of [Formula: see text] (let [Formula: see text], for [Formula: see text]), we show that a sequence in [Formula: see text], the unit ball in [Formula: see text], is interpolating for [Formula: see text] if and only if it is separated.

Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball

2013 ◽  
Vol 78 (2) ◽  
pp. 271-300 ◽  
Author(s):  
Wolfram Bauer ◽  
Crispin Herrera Yañez ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Radial Operators

Pluriharmonic Symbols of Commuting Toeplitz Type Operators on the Weighted Bergman Spaces

1998 ◽  
Vol 41 (2) ◽  
pp. 129-136 ◽  
Author(s):  
Young Joo Lee
Keyword(s):  
Unit Ball ◽  
Complex Space ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces

AbstractA class of Toeplitz type operators acting on the weighted Bergman spaces of the unit ball in the n-dimensional complex space is considered and two pluriharmonic symbols of commuting Toeplitz type operators are completely characterized.

BOUNDED TOEPLITZ AND HANKEL PRODUCTS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL

2015 ◽  
Vol 99 (2) ◽  
pp. 237-249
Author(s):  
MAŁGORZATA MICHALSKA ◽  
PAWEŁ SOBOLEWSKI
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Hankel Operator ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Necessary Condition ◽  
Sufficient Condition

Let $A_{{\it\alpha}}^{p}$ be the weighted Bergman space of the unit ball in ${\mathcal{C}}^{n}$, $n\geq 2$. Recently, Miao studied products of two Toeplitz operators defined on $A_{{\it\alpha}}^{p}$. He proved a necessary condition and a sufficient condition for boundedness of such products in terms of the Berezin transform. We modify the Berezin transform and improve his sufficient condition for products of Toeplitz operators. We also investigate products of two Hankel operators defined on $A_{{\it\alpha}}^{p}$, and products of the Hankel operator and the Toeplitz operator. In particular, in both cases, we prove sufficient conditions for boundedness of the products.

scholarly journals Volterra composition operators from generalized weighted weighted Bergman spaces toµ-Bloch spaces

2009 ◽  
Vol 7 (3) ◽  
pp. 225-240 ◽  
Author(s):  
Xiangling Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Composition Operators ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Bloch Spaces

Letφbe a holomorphic self-map andgbe a fixed holomorphic function on the unit ballB. The boundedness and compactness of the operatorTg,φf(z)=∫01f(φ(tz))ℜg(tz)dttfrom the generalized weighted Bergman space into the µ-Bloch space are studied in this paper.

scholarly journals On the cubic NLS on 3D compact domains

2013 ◽  
Vol 13 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Fabrice Planchon
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Schrodinger Equation ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Dirichlet Boundary Conditions ◽  
Well Posedness ◽  
Bounded Domains ◽  
Bilinear Estimates

AbstractWe prove bilinear estimates for the Schrödinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the ${ \mathbb{R} }^{3} $ case, while on bounded domains they match the generic boundaryless manifold case. We obtain, as an application, global well-posedness for the defocusing cubic NLS for data in ${ H}_{0}^{s} (\Omega )$, $1\lt s\leq 3$, with $\Omega $ any bounded domain with smooth boundary.

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