Let Gr(jc) be the Green function in a domain Ω Rm with a fixed pole, and Γ be an (m-1)-dimensional hyperplane. We give conditions on Ω and Ω∩Γ so that |∇G| is A∞ with respect to the (m-1)-dimensional measure on Ω ∩ Γ . Certain properties of the Riemann mapping of a simply-connected domain in R2 are extended to the Green function of domains in Rm.
|Original language||English (US)|
|Number of pages||20|
|Journal||Pacific Journal of Mathematics|
|State||Published - Jan 1993|
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