J. Pseudo-Differ. Oper. Appl. (2020) 11:1963–1989 https://doi.org/10.1007/s11868-019-00325-y Global regularity in Orlicz–Morrey spaces of solutions to parabolic equations with VMO coefficients Vagif Guliyev 1,2,3 · Ismail Ekincioglu 1 · Aysel Ahmadli 1 · Mehriban Omarova 3,4 Received: 3 October 2019 / Revised: 4 November 2019 / Accepted: 28 December 2019 / Published online: 7 January 2020 © Springer Nature Switzerland AG 2020 Abstract We show continuity in generalized parabolic Orlicz–Morrey spaces M Φ,ϕ of sublinear integral operators generated by parabolic Calderón–Zygmund operator and their com- mutators 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. Keywords Generalized parabolic Orlicz–Morrey spaces · Parabolic Calderón–Zygmund integrals · Commutators · VMO · Parabolic equations · Cauchy–Dirichlet problem Mathematics Subject Classification Primary 42B20; Secondary 35K20 · 46E30 B Vagif Guliyev vagif@guliyev.com Ismail Ekincioglu ismail.ekincioglu@dpu.edu.tr Aysel Ahmadli aysel.ahmadli@gmail.com Mehriban Omarova mehribanomarova@yahoo.com 1 Department of Mathematics, Dumlupinar University, Kutahya, Turkey 2 Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan 3 Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan 4 Baku State University, Baku, Azerbaijan