Powers of distances to lower dimensional sets as Muckenhoupt weights

Abstract

Let (X,d,mu) be an Ahlfors metric measure space. We give sufficient conditions on a closed set Fsubseteq X and on a real number eta in such a way that d(x,F)^beta becomes a Muckenhoupt weight. We give also some illustrations to regularity of solutions of partial differential equations and regarding some classical fractals.