Rudin orthogonality problem on the Bergman space

Gleason’s Problem in Weighted Bergman Space on Egg Domains

In the paper, we discuss on the egg domains: Ω a = ξ = (z, w) ∈ C n+m : z ∈ C n , w ∈ C m , |z| 2 + |w| 2/a < 1 , 0 < a ≤ 2. We show that Gleason's problem can be solved in the weight Bergman space on the egg domains. The proof will need the help of the recent work of the second named author on the weighted Bergman projections on this kind of domain. As an application, we obtain a multiplier th...

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...

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

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 ...