In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.

The boundedness of the difference of two weighted composition operators from weighted Bergman spaces to weighted-type spaces in the unit ball are investigated in this paper.

We introduce a family of weighted BMO spaces in the Bergman metric on the unit ball of C and use them to characterize complex functions f such that the big Hankel operators Hf and Hf̄ are both bounded or compact from a weighted Bergman space into a weighted Lesbegue space with possibly different exponents and different weights. As a consequence, when the symbol function f is holomorphic, we char...

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...

where the coefficients are entire functions. In [8], equations of the form (1) with coefficients in weighted Bergman or Hardy spaces are studied. The direct problem is proved, that is, if the coefficients aj(z), j = 0, ..., k − 1 of (1) belong to the weighted Bergman space, then all solutions are of finite order of growth and belong to weighted Bergman space. The inverse problem is also investi...

We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.

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...