On Seip’s Description of Sampling Sequences for Bergman Spaces

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

Weighted composition operators on weighted Bergman spaces and weighted Bloch spaces

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.

Double Integral Characterization for Bergman Spaces

‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...

Uniform Densities of Regular Sequences in the Unit Disk

The upper and lower uniform densities of some regular sequences are computed. These densities are used to determine sets of sampling and interpolation for Bergman spaces of the unit disk. §

On Uniformly Discrete Sequences in the Disk

We present an overview of uniformly discrete sequences and their relationship to other important types of sets, such as uniformly separated sequences, sets of interpolation and sampling, and zero-sets for Bergman spaces. Introduction A sequence Γ = {zk} in the unit disk D is said to be uniformly discrete if ρ(zj , zk) = ∣∣∣∣ zj − zk 1− zjzk ∣∣∣∣ ≥ δ for some fixed δ > 0 and all j 6= k. The supr...