Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension
Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension
Consider a standard Cantor set in the plane of Hausdorff dimension 1.If the linear density of the associated measure µ vanishes, then the set of points where the principal value of the Cauchy singular integral of µ exists has Hausdorff dimension 1.The result is extended to Cantor sets in R …