Expand all Collapse all | Results 1 - 6 of 6 |
1. CMB 2011 (vol 56 pp. 593)
On the $p$-norm of an Integral Operator in the Half Plane We give a partial answer to a conjecture of DostaniÄ on the
determination of the norm of a class of integral operators induced
by the weighted Bergman projection in the upper half plane.
Keywords:Bergman projection, integral operator, $L^p$-norm, the upper half plane Categories:47B38, 47G10, 32A36 |
2. 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 |
3. 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 |
4. CMB 2006 (vol 49 pp. 508)
Growth Spaces and Growth Norm Estimates for $\Bar\partial$ on Convex Domains of Finite Type We consider the growth norm of a measurable function $f$ defined by
$$\|f\|_{-\sigma}=\ess\{\delta_D(z)^\sigma|f(z)|:z\in D\},$$
where $\delta_D(z)$ denote the distance from $z$ to $\partial D$.
We prove some optimal growth norm estimates for $\bar\partial$
on convex domains of finite type.
Categories:32W05, 32A26, 32A36 |
5. 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 |
6. CMB 2003 (vol 46 pp. 559)
On Density Conditions for Interpolation in the Ball In this paper we study interpolating sequences for two related spaces of
holomorphic functions in the unit ball of $\C^n$, $n>1$. We first give density
conditions for a sequence to be interpolating for the class $A^{-\infty}$ of
holomorphic functions with polynomial growth. The sufficient condition is
formally identical to the characterizing condition in dimension $1$, whereas the
necessary one goes along the lines of the results given by Li and Taylor for
some spaces of entire functions. In the second part of the paper we show that a
density condition, which for $n=1$ coincides with the characterizing condition
given by Seip, is sufficient for interpolation in the (weighted) Bergman space.
Categories:32A36, 32A38, 30E05 |