Compact radial operators on the harmonic 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.

Positive Toeplitz Operators on the Bergman Space

In this paper we find conditions on the existence of bounded linear operators A on the Bergman space La(D) such that ATφA ≥ Sψ and ATφA ≥ Tφ where Tφ is a positive Toeplitz operator on L 2 a(D) and Sψ is a self-adjoint little Hankel operator on La(D) with symbols φ, ψ ∈ L∞(D) respectively. Also we show that if Tφ is a non-negative Toeplitz operator then there exists a rank one operator R1 on L ...

Intermediate Hankel Operators on the Bergman Space

Compact Composition Operators on Bergman Spaces of the Unit Ball

Under a mild condition we show that a composition operator Cφ is compact on the Bergman space Aα of the open unit ball in C if and only if (1− |z|)/(1− |φ(z)|) → 0 as |z| → 1−.

Toeplitz and Hankel Operators with Radial Symbol on the Bergman Space

Let dA denote Lebesgue area measure on the unit disk D, normalized so that the measure of D equals 1. For α > −1, we denote by dAα the measure dAα(z) = (α + 1)(1 − |z|2)αdA(z). For 1 ≤ p < +∞, the space L(D, dAα) is a Banach space. The weighted Bergman space Aα is the closed subspace of analytic functions in the Hilbert space L(D, dAα). For each z ∈ D, the application:Lz : A 2 α −→ C is continu...