Harmonic Bergman Functions on Half-spaces

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

Harmonic Bergman Kernel for Some Balls

We treat the complex harmonic function on the Np–ball which is defined by the Np–norm related to the Lie norm. As a subspace, we treat Hardy spaces and consider the Bergman kernel on those spaces. Then, we try to construct the Bergman kernel in a concrete form in 2–dimensional Euclidean space. Introduction. In [2], [4], [6] and [7], we studied holomorphic functions and analytic functionals on t...

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 $mathbb{C}^n$.

Duality between Harmonic and Bergman spaces

In this paper we study the duality of the harmonic spaces on the annulus Ω = Ω1 \Ω − between two pseudoconvex domains with Ω− ⊂⊂ Ω1 in Cn and the Bergman spaces on Ω−. We show that on the annulus Ω, the space of harmonic forms for the critical case on (0, n−1)-forms is infinite dimensional and it is dual to the the Bergman space on the pseudoconvex domain Ω−. The duality is further identified e...