HARMONIC ANALYSIS METHODS AND THE REGULARITY PROBLEM FOR PDE'S WITH DISCONTINUOUS DATA

Motivated by the extension of Calder ' on-Zygmund theory to the Lebesgue context, we study the boundedness of singular and nonsingular integral operators, and the associated commutators with VMO functions, on generalized Morrey spaces M-p,M-phi and generalized weighted Morrey spaces M-p,M-phi(w). We also show some applications to strong solutions to nondivergence elliptic equations with VMO coefficients.