TY - JOUR

T1 - A conformal inequality related to the conditional gauge theorem

AU - Mc Connell, Terry R.

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1990/4

Y1 - 1990/4

N2 - We prove the inequality h(x)−1 G(x, y)h(y) < cG(x, y) +c, where G is the Green function of a plane domain D, h is positive and harmonic on D, and c is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains c may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plane domains of finite area for which the constant c in the above inequality is finite.

AB - We prove the inequality h(x)−1 G(x, y)h(y) < cG(x, y) +c, where G is the Green function of a plane domain D, h is positive and harmonic on D, and c is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains c may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plane domains of finite area for which the constant c in the above inequality is finite.

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U2 - 10.1090/S0002-9947-1990-0957083-8

DO - 10.1090/S0002-9947-1990-0957083-8

M3 - Article

AN - SCOPUS:0041579895

SN - 0002-9947

VL - 318

SP - 721

EP - 733

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

ER -