Blaschke Sets for Bergman Spaces

A Survey of Linear Extremal Problems in Analytic Function Spaces

The purpose of this survey paper is to recall the major benchmarks of the theory of linear extremal problems in Hardy spaces and to outline the current status and open problems remaining in Bergman spaces. We focus on the model extremal problem of maximizing the norm of the linear functional associated with integration against a polynomial of finite degree, and discuss known solutions of partic...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

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...

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 $mathbb{C}^n$.

Pseudocontinuations and the Backward Shift

In this paper, we will examine the backward shift operator Lf = (f − f(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM ⊂M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L|M. In order to do this, we will use the concept of “pseudocontinuation” of functions across the...