Hausdorff measures, capacities and compact composition operators



Downloads per month over past year

Gallardo Gutiérrez, Eva A. and González, María J. (2006) Hausdorff measures, capacities and compact composition operators. Mathematische Zeitschrift, 253 (1). pp. 63-74. ISSN 0025-5874

[thumbnail of Gallardo16oficial.pdf] PDF
Restringido a Repository staff only


Official URL:


It is shown that there exist analytic self-maps phi of the unit disc D inducing compact composition operators on the Hardy space H-p, 1 <= p < infinity such that the Hausdorff dimension of the set E-omega = {e(i theta) is an element of partial derivative D: vertical bar phi(e(i theta))vertical bar = 1} is one; sharpening a classical result due to Schwartz. Moreover, the same holds in the weighted Dirichlet spaces D-alpha with 0 < alpha < 1. As a consequence, we deduce that there exist symbols. inducing compact composition operators on D-alpha such that the alpha-capacity of E-phi is positive, which is no longer true for those just inducing Hilbert-Schmidt composition operators on D-alpha.

Item Type:Article
Uncontrolled Keywords:composition operator; Weighted Dirichlet spaces; Hausdorff measures
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:21104
Deposited On:26 Apr 2013 08:32
Last Modified:10 Aug 2018 11:02

Origin of downloads

Repository Staff Only: item control page