Let 0 ≤ α < 1. Denote the open unit polydisk in C by ∆. We obtain a purely function-theoretic condition characterizing the holomorphic self-maps of ∆ that induce bounded composition operators on (1−α)-Bloch spaces, which we define on ∆. As a consequence, we extend Madigan’s characterization of bounded composition operators on analytic α-Lipschitz spaces over ∆ for 0 < α < 1 to an analogous char...

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.

In this article we prove that for any hyperbolic Riemann surface M of infinite analytic type, the little Bers space Q0(M) is isomorphic to c0. As a consequence of this result, if M is such a Riemann surface, then its asymptotic Teichmüller space AT (M) is bi-Lipschitz equivalent to a bounded open subset of the Banach space l∞/c0. Further, if M and N are two such Riemann surfaces, their asymptot...

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

We prove that a compact metric space (or more generally an analytic subset of a complete separable metric space) of Hausdorff dimension bigger than k can be always mapped onto a k-dimensional cube by a Lipschitz map. We also show that this does not hold for arbitrary separable metric spaces. As an application we essentially answer a question of Urbański by showing that the transfinite Hausdorff...

We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in R n. The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier work of D. Sullivan, our methods also yield an analytic characterization for smoothability of a Lipschitz manifold in terms of a Sobolev regularity for frames ...