Impacto
Downloads
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
![]() |
PDF
Restringido a Repository staff only 217kB |
Official URL: http://link.springer.com/content/pdf/10.1007%2Fs00209-005-0878-6.pdf
Abstract
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