Bergman projections on weighted Fock spaces in several complex variables

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

Zero Sets for Spaces of Analytic Functions

We show that under mild conditions, a Gaussian analytic function F that a.s. does not belong to a given weighted Bergman space or Bargmann–Fock space has the property that a.s. no non-zero function in that space vanishes where F does. This establishes a conjecture of Shapiro (1979) on Bergman spaces and allows us to resolve a question of Zhu (1993) on Bargmann–Fock spaces. We also give a simila...

Holomorphic Besov Spaces on Bounded Symmetric Domains, II

The paper continues the study of a class of holomorphic Besov spaces on bounded symmetric domains which was initiated in [18]. Several new descriptions of these Besov spaces are given in terms of weighted Bergman projections and fractional differential operators. These new characterizations are then applied to obtain results about the duality of, and Hankel operators on, weighted Bergman spaces...

Linear Differential Equations with Coefficients in Fock Type Space

where the coefficients are entire functions. In [8], equations of the form (1) with coefficients in weighted Bergman or Hardy spaces are studied. The direct problem is proved, that is, if the coefficients aj(z), j = 0, ..., k − 1 of (1) belong to the weighted Bergman space, then all solutions are of finite order of growth and belong to weighted Bergman space. The inverse problem is also investi...