Potentials on Special Open Sets

Abstract

Throughout this book a special open subset of ℝ^N is either a ball in ℝ^N or ℝ^N itself, but the latter only when N > 2. The Green function G _D for D a ball was defined in Section II.1. The Green function G _D for D = ℝ^N with N > 2 is defined as G. If μ is a measure on a special open set D, define the function G _D μ on D by

$$ {G_D}\mu (\zeta ) = \int_D {{G_D}(} \zeta, \eta )\mu (d\eta ) $$

(1.1)