GENERALIZED MORREY REGULARITY FOR PARABOLIC EQUATIONS WITH DISCONTINUOUS DATA

We prove continuity in generalized parabolic Morrey spaces M-p,M-phi of sublinear operators generated by the parabolic Calderon-Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. As a consequence, we obtain a global M-p,M-phi-regularity result for the Cauchy-Dirichlet problem for linear uniformly parabolic equations with vanishing mean oscillation (VMO) coefficients.