TY - JOUR
T1 - On the asymptotic behavior of condenser capacity under blaschke products and universal covering maps
AU - Betsakos, Dimitrios
AU - Kelgiannis, Georgios
AU - Kourou, Maria
AU - Pouliasis, And Stamatis
N1 - Funding Information:
Received by the editors October 7, 2018. 2010 Mathematics Subject Classification. Primary 30C85, 30J10, 30C80, 31A15. Key words and phrases. Condenser capacity, Lindelöf principle, Blaschke products, universal covering maps. This research has been co-financed by the Operational Program “Human Resources Development, Education and Lifelong Learning” and is co-financed by the European Union (European Social Fund) and Greek national funds.
Publisher Copyright:
©2019 American Mathematical Society.
PY - 2019
Y1 - 2019
N2 - We prove an estimate for the capacity of the condenser (D,Kr), r ∈ (0, 1), where D is the open unit disc and {Kr} is a compact exhaustion of the inverse image of a compact set under a Blaschke product B, involving weighted logarithmic integral means of the Frostman shifts of B. Also, we describe the asymptotic behavior of the capacity of condensers (D,Er), where Er is a connected component of the inverse image of a closed disc with radius r under universal covering maps as r → 0.
AB - We prove an estimate for the capacity of the condenser (D,Kr), r ∈ (0, 1), where D is the open unit disc and {Kr} is a compact exhaustion of the inverse image of a compact set under a Blaschke product B, involving weighted logarithmic integral means of the Frostman shifts of B. Also, we describe the asymptotic behavior of the capacity of condensers (D,Er), where Er is a connected component of the inverse image of a closed disc with radius r under universal covering maps as r → 0.
KW - Blaschke products
KW - Condenser capacity
KW - Lindelöf principle
KW - Universal covering maps
UR - http://www.scopus.com/inward/record.url?scp=85070629905&partnerID=8YFLogxK
U2 - 10.1090/proc/14585
DO - 10.1090/proc/14585
M3 - Article
AN - SCOPUS:85070629905
SN - 0002-9939
VL - 147
SP - 2963
EP - 2973
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 7
ER -