Generalized Morrey regularity for parabolic equations with discontinuity data

Abstract: We obtain continuity in generalized parabolic Morrey spaces of sublinear integrals generated by the parabolic Calder\'{o}n-Zygmund operators and its commutator with $VMO$ functions. The obtained estimates are used to study global regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations with discontinuous coefficients.