On the boundary limits of Green potentials of functions
Let \(D=\{x\in R^ n:\) \(x_ n>0\}\) and let G(x,y) be the Green function in D. For a nonnegative measurable function f on D with \[ (1)\quad \int_{D}(1+| y|)^{-n} y_ nf(y) dy<\infty. \] Put \(GF(x)=\int_{D}G(x,y)f(y)dy.\) The author studies the existence of the non-tangential limits of the Green potential Gf under the condition (1) and under an additional condition on the function f depending on a calibration function \(\omega\). Under these two conditions the author shows, extending a result of K.-O. Widman (1967), that Gf has non-tangential limits on \(\partial D\setminus E\) where E has zero Hausdorff h-measure with h depending on \(\omega\).
scientific article; zbMATH DE number 4138132