Mean Lipschitz conditions on Bergman space

Lipschitz Type Characterizations for Bergman Spaces

We obtain new characterizations for Bergman spaces with standard weights in terms of Lipschitz type conditions in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we prove optimal embedding theorems when an analytic function on the unit disk is symmetrically lifted to the bidisk.

On the character space of vector-valued Lipschitz algebras

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

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 ...

Composition Operator on Bergman-Orlicz Space

Recommended by Shusen Ding Let D denote the open unit disk in the complex plane and let dAz denote the normalized area measure on D. Φ α is defined as follows L Φ α {f ∈ HD : D ΦΦlog |fz|1 − |z| 2 α dAz < ∞}. Let ϕ be an analytic self-map of D. The composition operator C ϕ induced by ϕ is defined by C ϕ f f • ϕ for f analytic in D. We prove that the composition operator C ϕ is compact on L Φ α ...

Intermediate Hankel Operators on the Bergman Space