Estimates of the Besov norms on the fractal boundary and applications

Abstract

Let u be a λ-Hölder continuous function on the closure of a bounded domain D with fractal boundary ∂ D. We estimate the Besov norm of the restriction of u to ∂ D by the L^p(D)-norm of |∇ u(y)| dist (y, ∂ D)^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 ∂ D.