Singular Integrals and Potential Theory

摘要

In this paper I consider a class of non-standard singular integrals motivated by potential theoretic and probabilistic considerations. The probabilistic applications, which are by far the most interesting part of this circle of ideas, are only outlined in Section 1.5: They give the best approximation of the solution of the classical Dirichlet problem in a Lipschitz domain $Omegasubset {mathbb{R}}^{n+1}$ by the corresponding solution by finite differences.