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1. CMB 2011 (vol 55 pp. 146)
A Characterization of Bergman Spaces on the Unit Ball of ${\mathbb C}^n$. II It has been shown that a holomorphic function $f$ in the unit ball
$\mathbb{B}_n$ of ${\mathbb C}_n$ belongs to the weighted Bergman space $A^p_\alpha$,
$p>n+1+\alpha$, if and only if the function
$|f(z)-f(w)|/|1-\langle z,w\rangle|$ is in $L^p(\mathbb{B}_n\times\mathbb{B}_n,dv_\beta
\times dv_\beta)$, where $\beta=(p+\alpha-n-1)/2$ and $dv_\beta(z)=
(1-|z|^2)^\beta\,dv(z)$. In this paper
we consider the range $0
n+1+\alpha$ is particularly interesting. Keywords:Bergman spaces, unit ball, volume measure Category:32A36 |
2. CMB 2009 (vol 52 pp. 613)
Lipschitz Type Characterizations for Bergman Spaces We obtain new characterizations for Bergman spaces with standard
weights in terms of Lipschitz type conditions in the Euclidean,
hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we
prove optimal embedding theorems when an analytic function
on the unit disk is symmetrically lifted to the bidisk.
Keywords:Bergman spaces, hyperbolic metric, Lipschitz condition Category:32A36 |
3. CMB 2006 (vol 49 pp. 381)
On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain |
On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain It is known that the derivative of
a Blaschke product whose zero sequence lies in a Stolz angle
belongs to all the Bergman spaces $A^p$ with $0
1$). As a consequence, we prove that there exists a Blaschke product $B$ with zeros on a radius such that $B'\notin A^{3/2}$. Keywords:Blaschke products, Hardy spaces, Bergman spaces Categories:30D50, 30D55, 32A36 |
4. CMB 1998 (vol 41 pp. 129)
Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces A 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.
Keywords:Pluriharmonic functions, Weighted Bergman spaces, Toeplitz type operators. Categories:47B38, 32A37 |