Factorization of functions in weighted Bergman spaces
Hankel operators and the Dixmier trace on strictly pseudoconvex domains.
Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains
On complete pseudoconvex Reinhardt domains in , we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite...
Hölder functions in Bergman type spaces
It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth of its derivative....
Kernels of Toeplitz operators on the Bergman space
A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.
Lp continuity of projectors of weighted harmonic Bergman spaces.
m-Berezin transform and compact operators.
m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L∞ is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary...
New characterizations of Bergman spaces.
On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball.
On an integral operator on the unit ball in .
On an integral-type operator from Zygmund-type spaces to mixed-norm spaces on the unit ball.
On boundary behaviour of the Bergman projection on pseudoconvex domains
It is shown that on strongly pseudoconvex domains the Bergman projection maps a space of functions growing near the boundary like some power of the Bergman distance from a fixed point into a space of functions which can be estimated by the consecutive power of the Bergman distance. This property has a local character. Let Ω be a bounded, pseudoconvex set with C³ boundary. We show that if the Bergman projection is continuous on a space defined by weighted-sup seminorms and equipped with the topology...
On locally convex extension of in the unit ball and continuity of the Bergman projection
We define locally convex spaces LW and HW consisting of measurable and holomorphic functions in the unit ball, respectively, with the topology given by a family of weighted-sup seminorms. We prove that the Bergman projection is a continuous map from LW onto HW. These are the smallest spaces having this property. We investigate the topological and algebraic properties of HW.
On self-commutators of Toeplitz operators with rational symbols
We prove that the self-commutator of a Toeplitz operator with unbounded analytic rational symbol has a dense domain in both the Bergman space and the Hardy space of the unit disc. This is a basic step towards establishing whether the self-commutator has a compact or trace-class extension.
On some properties of a differential operator on the polydisk.
On the Toëplitz corona problem.
The aim of this note is to characterize the vectors g = (g1, . . . ,gk) of bounded holomorphic functions in the unit ball or in the unit polydisk of Cn such that the Corona is true for them in terms of the H2 Corona for measures on the boundary.
Quasiconformal deformations of holomorphic functions.
Removable singularities for weighted Bergman spaces
We develop a theory of removable singularities for the weighted Bergman space , where is a Radon measure on . The set is weakly removable for if , and strongly removable for if . The general theory developed is in many ways similar to the theory of removable singularities for Hardy spaces, and locally Lipschitz spaces of analytic functions, including the existence of counterexamples to many plausible properties, e.g. the union of two compact removable singularities needs not be removable....
Schatten class Toeplitz operators on weighted Bergman spaces of the unit ball.
Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains
We characterize the Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains in terms of the Berezin transform.