Sampling with Derivatives in the Bergman Space

Self-commutators of composition operators with monomial symbols on the Bergman space

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...

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

The Homogeneous Approximation Property in the Bergman Space

It is shown that sets of sampling for the Bergman space A2 have the “homogeneous approximation property” (HAP) and that sets with this property are sampling for A 2+E. In addition, previous results concerning the boundary behaviour of sampling sets are improved. ForO<p<oo, the Bergman space AP is the set of functions f analytic in the unit disk D = (2 : 1.~1 < 1) with where dA denotes Lebesgue ...

Weighted Two-parameter Bergman Space Inequalities

In this inequality, ∇ denotes the full gradient in R + : ∇ = (∂/∂x1, . . . , ∂/∂xd, ∂/∂y); R + is the usual upper half space Rd×(0,∞); μ is a positive Borel measure defined on R + ; and v is a non-negative function in Lloc(R d). We studied this inequality primarily for p and q in the range 1 < p ≤ q < ∞. For the case in which q ≥ 2, we proved sufficient conditions on μ and v (depending on p, q,...