Global regularity in Orlicz–Morrey spaces of solutions to parabolic equations with VMO coefficients

We show continuity in generalized parabolic Orlicz–Morrey spaces M Φ , φ of sublinear integral operators generated by parabolic Calderón–Zygmund operator and their commutators with BMO functions. As a consequence, we obtain a global M Φ , φ -regularity result for the Cauchy–Dirichlet problem for linear uniformly parabolic equations with vanishing mean oscillation coefficients.