Željko Čučković

Commuting Toeplitz operators with harmonic symbols

This paper shows that on the Bergman space, two Toeplitz operators with harmonic symbols commute only in the obvious cases. The main tool is a characterization of harmonic functions by a conformally invariant mean value property.

Toeplitz operators on Bergman spaces of polyanalytic functions

We study algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions on the unit disk. We obtain results on finite-rank commutators and semi-commutators of Toeplitz operators with harmonic symbols. We also raise and discuss some open questions.

Berezin versus Mellin

We study zero products of two Bergman space Toeplitz operators, where one symbol is harmonic. Our results point in the direction of the zero product problem having only a trivial solution. The techniques we use are based on a formula that connects the Berezin and Mellin transform.

Special Toeplitz operators on strongly pseudoconvex domains

Toeplitz operators on strongly pseudoconvex domains in Cn, constructed from the Bergman projection and with symbol equal to a positive power of the distance to the boundary, are considered. The mapping properties of these operators on Lp, as the power of the distance varies, are established

Toeplitzness of composition operators in several variables

Motivated by the work of Nazarov and Shapiro on the unit disk, we study asymptotic Toeplitzness of composition operators on the Hardy space of the unit sphere in . We extend some of their results but we also show that new phenomena appear in higher dimensions.