Estimates of the Besov norms on the fractal boundary and applications

摘要

Let u be a λ-Hoelder continuous function on the closure of a bounded domain D with fractal boundary partial derivD. We estimate the Besov norm of the restriction of u to partial derivD by the L~p(D)-norm of |▽u(y)|dist(y, partial derivD)~λ for an adequate λ > 0. We apply it to the boundedness of operators related to the double layer potentials on the Besov spaces on partial derivD.