The pseudohyperbolic metric and Bergman spaces in the ball

The Pseudohyperbolic Metric and Bergman Spaces in the Ball

The pseudohyperbolic metric is developed for the unit ball of Cn and is applied to a study of uniformly discrete sequences and Bergman spaces of holomorphic functions on the ball. The pseudohyperbolic metric plays an important role in the study of Bergman spaces over the unit disk. It is defined in terms of Möbius self-mappings of the disk. As is well known, these conformal automorphisms genera...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

Compact Composition Operators on Bergman Spaces of the Unit Ball

Under a mild condition we show that a composition operator Cφ is compact on the Bergman space Aα of the open unit ball in C if and only if (1− |z|)/(1− |φ(z)|) → 0 as |z| → 1−.

on some properties of analytic spaces connected with bergman metric ball

Ball transitive ordered metric spaces

0. Introduction. If (X,≤) is a partially ordered set and A ⊆ X, then the decreasing hull d(A) of A in X is defined to be d(A) = {x ∈ X : x ≤ a for some a ∈ A}. If the poset X is not understood from the context, we may write dX(A). A subset A ⊆ X is a decreasing set if A = d(A). The intersection or union of any collection of decreasing sets in X is again a decreasing set in X. The increasing hul...