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.