Global Regularity In Weighted Morrey-Herz Spaces Of Solutions To Nondivergence Elliptic Equations With VMO Coefficients

There are three chapters in this paper. By establishing the boundedness re-sults of singular integral operators and their commutators, we obtain the global regularity of strong solutions to nondivergence elliptic equations with VMO coeffi-cients in weighted Morrey-Herz spaces. The first chapter is an overview of weighted Morrey-Herz spaces. The second chapter mainly discusses the boundedness of C-Z type operators and their commutators in weighted Morrey-Herz spaces. The third chapter mainly studies the global regularity of the strong solutions to second-order nondivergence elliptic equations of Dirichlet problem in weighted Morrey-Herz s-paces.