Interpolating sequences for the derivatives of Bloch functions

1992 ◽  
Vol 34 (1) ◽  
pp. 35-41 ◽  
Author(s):  
K. R. M. Attele
Keyword(s):  
Bergman Space ◽  
Hankel Operator ◽  
Essential Norm ◽  
Bloch Function ◽  
Sufficient Condition ◽  
Bloch Functions ◽  
Interpolating Sequences ◽  
Analytic Symbol ◽  
Derivatives Of

AbstractWe prove that sufficiently separated sequences are interpolating sequences for f′(z)(1−|z|2) where f is a Bloch function. If the sequence {zn} is an η net then the boundedness f′(z)(1−|z|2) on {zn} is a sufficient condition for f to be a Bloch function. The essential norm of a Hankel operator with a conjugate analytic symbol acting on the Bergman space is shown to be equivalent to .

scholarly journals Essential norm estimates for Hankel operators on convex domains in $\mathbb{C}^2$

2017 ◽  
Vol 120 (2) ◽  
pp. 305
Author(s):  
Željko Čučković ◽  
Sönmez Şahutoğlu
Keyword(s):  
Convex Domain ◽  
Hankel Operator ◽  
Smooth Boundary ◽  
Essential Norm ◽  
Hankel Operators ◽  
Convex Domains ◽  
Norm Estimates ◽  
Bounded Convex Domain ◽  
Derivatives Of ◽  
Bounded Convex

Let $\Omega \subset \mathbb{C}^2$ be a bounded convex domain with $C^1$-smooth boundary and $\varphi \in C^1(\overline{\Omega})$ such that $\varphi $ is harmonic on the non-trivial disks in the boundary. We estimate the essential norm of the Hankel operator $H_{\varphi }$ in terms of the $\overline{\partial}$ derivatives of $\varphi$ “along” the non-trivial disks in the boundary.

scholarly journals The Essential Norm of the Generalized Hankel Operators on the Bergman Space of the Unit Ball inCn

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Luo Luo ◽  
Yang Xuemei
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Hankel Operator ◽  
Equivalent Form ◽  
Essential Norm ◽  
Hankel Operators

In 1993, Peloso introduced a kind of operators on the Bergman spaceA2(B)of the unit ball that generalizes the classical Hankel operator. In this paper, we estimate the essential norm of the generalized Hankel operators on the Bergman spaceAp(B)  (p>1)of the unit ball and give an equivalent form of the essential norm.

The essential norm of Hankel operator on the Bergman space

1993 ◽  
Vol 17 (3) ◽  
pp. 361-372 ◽  
Author(s):  
Peng Lin ◽  
Richard Rochberg
Keyword(s):  
Bergman Space ◽  
Hankel Operator ◽  
Essential Norm

scholarly journals Finite rank intermediate Hankel operators and the big Hankel operator

2006 ◽  
Vol 2006 ◽  
pp. 1-3 ◽  
Author(s):  
Tomoko Osawa
Keyword(s):  
Bergman Space ◽  
Finite Rank ◽  
Hankel Operator ◽  
Closed Subspace ◽  
Hankel Operators ◽  
Coordinate Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

LetLa2be a Bergman space. We are interested in an intermediate Hankel operatorHφMfromLa2to a closed subspaceMofL2which is invariant under the multiplication by the coordinate functionz. It is well known that there do not exist any nonzero finite rank big Hankel operators, but we are studying same types in caseHφMis close to big Hankel operator. As a result, we give a necessary and sufficient condition aboutMthat there does not exist a finite rankHφMexceptHφM=0.

On derivatives of fuzzy multi-dimensional mappings and applications under generalized differentiability

2021 ◽  
pp. 1-19
Author(s):  
M. Miri Karbasaki ◽  
M. R. Balooch Shahriari ◽  
O. Sedaghatfar
Keyword(s):  
Linear Function ◽  
Level Set ◽  
Fuzzy Numbers ◽  
Sufficient Condition ◽  
Continuous Linear ◽  
Generalized Differentiability ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of ◽  
Dimensional Mapping

This article identifies and presents the generalized difference (g-difference) of fuzzy numbers, Fréchet and Gâteaux generalized differentiability (g-differentiability) for fuzzy multi-dimensional mapping which consists of a new concept, fuzzy g-(continuous linear) function; Moreover, the relationship between Fréchet and Gâteaux g-differentiability is studied and shown. The concepts of directional and partial g-differentiability are further framed and the relationship of which will the aforementioned concepts are also explored. Furthermore, characterization is pointed out for Fréchet and Gâteaux g-differentiability; based on level-set and through differentiability of endpoints real-valued functions a characterization is also offered and explored for directional and partial g-differentiability. The sufficient condition for Fréchet and Gâteaux g-differentiability, directional and partial g-differentiability based on level-set and through employing level-wise gH-differentiability (LgH-differentiability) is expressed. Finally, to illustrate the ability and reliability of the aforementioned concepts we have solved some application examples.

scholarly journals The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

2021 ◽  
Author(s):  
Cezhong Tong ◽  
Junfeng Li ◽  
Hicham Arroussi
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Kernel Estimates ◽  
Berezin Transforms

AbstractIn this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.

scholarly journals Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Roberto C. Raimondo
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Boundary Behavior ◽  
Berezin Transform ◽  
Planar Domain ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Planar Domains ◽  
Necessary And Sufficient ◽  
The Relationship

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

scholarly journals Interpolating sequences for the Bergman space.

1994 ◽  
Vol 41 (1) ◽  
pp. 73-86 ◽  
Author(s):  
Ke He Zhu
Keyword(s):  
Bergman Space ◽  
Interpolating Sequences

scholarly journals ESSENTIAL NORM OF EXTENDED CESÀRO OPERATORS FROM ONE BERGMAN SPACE TO ANOTHER

2011 ◽  
Vol 85 (2) ◽  
pp. 307-314 ◽  
Author(s):  
ZHANGJIAN HU
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Normal Weight ◽  
Cesàro Operator ◽  
Radial Derivative ◽  
Image Position ◽  
Cesaro Operator

AbstractLet Ap(φ) be the pth Bergman space consisting of all holomorphic functions f on the unit ball B of ℂn for which $\|f\|^p_{p,\varphi }= \int _B |f(z)|^p \varphi (z) \,dA(z)\lt +\infty $, where φ is a given normal weight. Let Tg be the extended Cesàro operator with holomorphic symbol g. The essential norm of Tg as an operator from Ap (φ) to Aq (φ) is denoted by $\|T_g\|_{e, A^p (\varphi )\to A^q (\varphi )} $. In this paper it is proved that, for p≤q, with 1/k=(1/p)−(1/q) , where ℜg(z) is the radial derivative of g; and for p>q, with 1/s=(1/q)−(1/p) .

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