Majorization and domination in the Bergman space

Stochastic domination for iterated convolutions and catalytic majorization

We study how iterated convolutions of probability measures compare under stochastic domination. We give necessary and sufficient conditions for the existence of an integer n such that μ is stochastically dominated by ν for two given probability measures μ and ν. As a consequence we obtain a similar theorem on the majorization order for vectors in R. In particular we prove results about catalysi...

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 ...

The Bergman Spaces, the Bloch Space, and Gleason's Problem

Suppose / is a holomorphic function on the open unit ball Bn of Cn. For 1 < p < oo and to > 0 an integer, we show that / is in Lp(Bn,dV) (with dV the volume measure) iff all the functions dmf/dza (\a\ = to) are in Lp(Bn,dV). We also prove that / is in the Bloch space of Bn iff all the functions dmf/dza (\a\ = m) are bounded on Bn. The corresponding result for the little Bloch space of Bn is est...