We prove that the boundedness and compactness of the Toeplitz operator on the Bergman space with a BMO 1 symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends the known results in the cases when the symbol is either a positive L 1-function or an L ∞ function. 1. Introduction. Toeplitz operators are one of the most widely studied classes of concr...

We study the boundedness and compactness of generalized Volterra integral operator on weighted Bergman spaces with doubling weights unit disc. A Toeplitz is defined boundedness, Schatten class membership this are investigated Hilbert space. As an application, operators also characterized. Finally, we get characterizations Hardy space $$H^2$$ .

We characterize the symbols φ for which there exists a weight w such that weighted composition operator MwCφ is compact on Bergman space Bα2. also bounded but not compact. investigate when Hilbert-Schmidt

Preface The book is devoted to the spectral theory of commutative C *-algebras of Toeplitz operators on Bergman spaces, and its applications. For each such commutative algebra we construct a unitary operator which reduces each Toeplitz operator from this algebra to a certain multiplication operator, thus also providing its spectral type representation. This gives us a powerful research tool all...

In this Erratum we would like to clarify statement and the proof of Theorem 2 in our paper: ”Zero-based invariant subspaces Bergman space Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 67(1) (2018), 277-285.”

An analogue of the notion of uniformly separated sequences, expressed in terms of canonical divisors, is shown to yield a necessary and sufficient condition for interpolation in the Bergman space Ap, 0 < p < ∞. A sequence Γ = {zj} of distinct points in the open unit disk D = {z : |z| < 1} of the complex plane is a classical interpolation sequence if for every bounded sequence {aj}, there is a b...