Canonical Divisors in Weighted Bergman Spaces

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 $mathbb{C}^n$.

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

Zeros of Extremal Functions in Weighted Bergman Spaces

For −1 < α ≤ 0 and 0 < p < ∞, the solutions of certain extremal problems are known to act as contractive zerodivisors in the weighted Bergman space Aα. We show that for 0 < α ≤ 1 and 0 < p < ∞, the analogous extremal functions do not have any extra zeros in the unit disk and, hence, have the potential to act as zero-divisors. As a corollary, we find that certain families of hypergeometric funct...

The Canonical Solution Operator to ∂ Restricted to Bergman Spaces and Spaces of Entire Functions

Abstract. In this paper we obtain a necessary and sufficient condition for the canonical solution operator to ∂ restricted to radial symmetric Bergman spaces to be a Hilbert-Schmidt operator. We also discuss compactness of the solution operator in spaces of entire functions in one variable. In the sequel we consider several examples and also treat the case of weighted spaces of entire functions...

Ample Divisors on M 0,a (with Applications to Log Mmp for M 0,n )

We introduce a new technique for proving positivity of certain divisor classes on M0,n and its weighted variants M0,A. Our methods give an unconditional description of the symmetric weighted spaces M0,A as log canonical models of M0,n.