A Conformal Inequality Related to the Conditional Gauge Theorem
A Conformal Inequality Related to the Conditional Gauge Theorem
We prove the inequality h(x)~ 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 …