INTEGRABILITY OF GREEN POTENTIALS IN FRACTAL DOMAINS

We prove L(q)-inequalities for the gradient of the Green potential (Gf ) in bounded, connected NTA-domains in R(n), n greater than or equal t o 2. These domains may have a highly non-rectifiable boundary and in t he plane the set of all bounded simply connected NTA-domains coincides with the set of all quasidiscs. We get a restriction on the exponent q for which our inequalities are valid in terms of the validity of a r everse Holder inequality for the Green function close to the boundary.