In this paper we consider a class of weighted integral operators on L2(0,∞) and show that they are unitarily equivalent to little Hankel operators between weighted Bergman spaces of the right half plane. We use two parameters α, β ∈ (−1,∞) and involve two weights to define Bergman spaces of the domain and range of the little Hankel operators. We obtained conditions for the Hankel integral opera...

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...

We consider differences of weighted composition operators between given weighted Bergman spaces H∞ v of infinite order and characterize boundedness and the essential norm of these differences.

In this paper we study the boundedness of composition operators on weighted Bergman spaces and Hardy space over polydisc Dn. Studying volume sublevel sets show for which n necessary conditions obtained by Bayart are sufficient. For arbitrary prove rank sufficiency theorem which, in particular, provides us with a simple criterion describing bidisc. Such consistent characterization is classical t...

We prove that Bergman projections on weighted mixed norm spaces smoothly bounded domains in $\mathbb{R}^n$ are for a certain range of parameters such and assuming conditions weights. The proof relies estimates integral means $M_p(P_\gamma f, r)$ terms $f$. This result complements earlier boundedness $P_\gamma$ closely related space $L^{p,q}_\alpha(\Omega).$

Any analytic self-map of the open unit disk induces a bounded composition operator on the Hardy space H and on the standard weighted Bergman spaces Aα. For a particular self-map, it is reasonable to wonder whether there is any meaningful relationship between the norms of the corresponding operators acting on each of these spaces. In this paper, we demonstrate an inequality which, at least to a ...

We present here a quite unexpected result: Apart from already known commutative C∗-algebras generated by Toeplitz operators on the unit ball, there are many other Banach algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C∗-algebra, and for n = 1 all of them ...