Weighted estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications (Q6564163)

This paper gives some weighted norm estimates for commutators with BMO coefficients of singular operators in local generalized Morrey spaces, where the used weights are certain radial weights which may be beyond the Muckenhoupt range. As a consequence of these estimates, a norm inequality for these commutators in the generalized Stummel-Morrey spaces is obtained. Then, via the embedding from some weighted Morrey spaces into Lebesgue spaces, the author proves the applicability of a well-known representation formula for the second-order derivatives of solutions to elliptic PDEs in the weighted Morrey space. Using this and the previous weighted norm estimates, the interior regularity for solutions of some elliptic PDEs in the frameworks of the corresponding weighted Sobolev spaces based on the local generalized Morrey spaces or Stummel-Morrey spaces is then obtained.