1. CMB 2012 (vol 56 pp. 241)
|Versions of Schwarz's Lemma for Condenser Capacity and Inner Radius|
We prove variants of Schwarz's lemma involving monotonicity properties of condenser capacity and inner radius. Also, we examine when a similar monotonicity property holds for the hyperbolic metric.
Keywords:condenser capacity, inner radius, hyperbolic metric, Schwarz's lemma
Categories:30C80, 30F45, 31A15
2. CMB 2009 (vol 52 pp. 613)
|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.
Keywords:Bergman spaces, hyperbolic metric, Lipschitz condition