Regularity in generalized Morrey spaces of solutions to higher order nondivergence elliptic equations with VMO coefficients

Abstract

We study the boundedness of the sublinear integral operators generated by Calderón–Zygmund operator and their commutators with $\mathit{BMO}$ functions on generalized Morrey spaces. These obtained estimates are used to get regularity of the solution of Dirichlet problem for higher order linear elliptic operators.

Keywords

• higher order elliptic equations
• generalized morrey spaces
• calderón–zygmund integrals
• commutators
• vmo