Weighted norm inequalities for fractional operators]

Abstract

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-$\lambda$ method that does not use any size or smoothness estimates for the kernels.

arXiv commentaccepted in Indiana University Mathematicla Journal. A thorough reorganisation has been done on suggestions from the referee