Binormal measures

Abstract

Our starting point is the measure ${\epsilon }_x-{\alpha }_x{\rho }_x^{{\omega }_1}+{\beta }_x{\rho }_x^{{\omega }_2}$, where ${\rho }_x^{{\omega }_i}$ is the harmonic measure relative to $x\in {\omega }_1\subset {\overline{\omega }}_1\subset {\omega }_2$ and ${\omega }_i$ are concentric balls of ${\mathbb{R}}^n$; ${\alpha }_x$, ${\beta }_x$ are functions depending on $x$ and on the radii of ${\omega }_i$, $(i=1,2)$. Generalizing the above measure, we introduce and study the binormal measures as well as their relation to biharmonic functions.