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

VL - 147

SP - 2963

EP - 2973

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -