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 - 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 -