Quantities equivalent to the norm of a weighted Bergman space

An equivalent representation for weighted supremum norm on the upper half-plane

In this paper, rstly, we obtain some inequalities which estimates complex polynomials on the circles.Then, we use these estimates and a Moebius transformation to obtain the dual of this estimates forthe lines in upper half-plane. Finally, for an increasing weight on the upper half-plane withcertain properties and holomorphic functions f on the upper half-plane we obtain an equivalentrepresenta...

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,...

Hankel Operators on Weighted Bergman Spaces and Norm Ideals

Consider Hankel operators Hf on the weighted Bergman space L 2 a(B, dvα). In this paper we characterize the membership of (H∗ fHf ) s/2 = |Hf | in the norm ideal CΦ, where 0 < s ≤ 1 and the symmetric gauge function Φ is allowed to be arbitrary.

Two Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane

Introduction In this paper, we intend to show that without any certain growth condition on the weight function, we always able to present a weighted sup-norm on the upper half plane in terms of weighted sup-norm on the unit disc and supremum of holomorphic functions on the certain lines in the upper half plane. Material and methods We use a certain transform between the unit dick and the uppe...

Composition Operators from the Weighted Bergman Space to the nth Weighted Spaces on the Unit Disc