BMOand Hankel operators on Bergman spaces

Hankel Operators on Weighted Bergman Spaces and Norm Ideals

Consider Hankel operators Hf on the weighted Bergman space L 2 a(B, dvα). In this paper we characterize the membership of (H∗ fHf ) s/2 = |Hf | in the norm ideal CΦ, where 0 < s ≤ 1 and the symmetric gauge function Φ is allowed to be arbitrary.

Weighted Bmo and Hankel Operators between Bergman Spaces

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...

Intermediate Hankel Operators on the Bergman Space

Compact Operators on Bergman Spaces

We prove that a bounded operator S on La for p > 1 is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disk if S satisfies some integrable conditions. Some estimates about the norm and essential norm of Toeplitz operators with symbols in BT are obtained.

Operators on weighted Bergman spaces

Let ρ : (0, 1] → R+ be a weight function and let X be a complex Banach space. We denote by A1,ρ(D) the space of analytic functions in the disc D such that ∫ D |f(z)|ρ(1 − |z|)dA(z) < ∞ and by Blochρ(X) the space of analytic functions in the disc D with values in X such that sup|z|<1 1−|z| ρ(1−|z|)‖F ′(z)‖ < ∞. We prove that, under certain assumptions on the weight, the space of bounded operator...