On precise differentiation formula for weighted singular integrals of Sobolev functions The paper is dedicated to professor Lars-Erik Persson, on the occasion of his 70th birthday

摘要

In various applications there appear integral equations of the first kind with a kernel which has a logarithmic singularity. The corresponding classes of well-posedness for such equations are Sobolev spaces. We prove the differentiation formulas for weighted singular integrals, which appear in such study, with the goal of its further application to integral equations.