A conformal inequality related to the conditional gauge theorem

Autor:	Terry R. McConnell
Rok vydání:	1990
Předmět:	Pure mathematics Harmonic function Plane (geometry) Applied Mathematics General Mathematics Domain (ring theory) Simply connected space Mathematical analysis Conformal map Gauge (firearms) Constant (mathematics) Brownian motion Mathematics
Zdroj:	Transactions of the American Mathematical Society. 318:721-733
ISSN:	1088-6850 0002-9947
DOI:	10.1090/s0002-9947-1990-0957083-8
Popis:	We prove the inequality h ( x ) − 1 G ( x , y ) h ( y ) ⩽ c G ( x , y ) + c h{(x)^{ - 1}}G(x,y)h(y) \leqslant cG(x,y) + c , where G G is the Green function of a plane domain D , h D,\;h is positive and harmonic on D D , and c 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 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 c in the above inequality is finite.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::584b9ed6b6b43bda3361b44f7eaf1bf9 https://doi.org/10.1090/s0002-9947-1990-0957083-8 Zobrazit plný text záznamu