Some inequalities and embeddings for weighted W0 spaces on domains with fractal boundaries

If Omega is a finite measure domain we show that several Poincare, Hardy-type, or multiplicative inequalities as well as classical Sobolev embedding theorems on W-0(m,p) (Omega) may be extended to versions with singular or degenerate weights involving powers of the distance to the boundary function provided that partial derivativeOmega is "fractal" in the sense that partial derivativeOmega has interior Minkowski dimension (M) over tilde (D)(partial derivativeOmega) < n. For unbounded non-finite measure domains such extensions may also often be made if partial derivativeOmega satisfies a certain definition of "locally fractal".