Global regularity in Orlicz-Morrey spaces of solutions to parabolic equations with VMO coefficients. (English) Zbl 1451.42020
Summary: We show continuity in generalized parabolic Orlicz-Morrey spaces \(M^{\varPhi ,\varphi }\) of sublinear integral operators generated by parabolic Calderón-Zygmund operator and their commutators with BMO functions. As a consequence, we obtain a global \(M^{\varPhi ,\varphi } \)-regularity result for the Cauchy-Dirichlet problem for linear uniformly parabolic equations with vanishing mean oscillation coefficients.
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B37 | Harmonic analysis and PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
Keywords:
generalized parabolic Orlicz-Morrey spaces; parabolic Calderón-Zygmund integrals; commutators; VMO; parabolic equations; Cauchy-Dirichlet problemReferences:
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