Duality of Holomorphic Function Spaces and Smoothing Properties of the Bergman Projection

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...

Composition Operators and Isometries on Holomorphic Function Spaces over Domains in C

Let D be a bounded domain in C with C boundary. Many holomorphic function spaces over D have been introduced in last half century, such as Hardy, Bergman, Besov and Sobolev spaces. Properties (boundary behaviour ect.) of functions in those function spaces have been received a great deal of studies. Readers can see parts of them from the following books [26] [29], [66], [71], [75], [76] and refe...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles

‎In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle‎. ‎We prove optimal estimates for the mapping properties of the Bergman projection on these domains.

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...