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.

中文翻译：

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具有VMO系数的抛物方程的解的Orlicz-Morrey空间中的整体正则性

我们在由抛物线式Calderón-Zygmund算子及其带有BMO函数的换向子产生的次线性积分算子的广义抛物Orlicz-Morrey空间\（M ^ {\ varPhi，\ varphi} \）中显示连续性。结果，对于平均振荡系数消失的线性一致抛物方程的Cauchy-Dirichlet问题，我们获得了一个整体\（M ^ {\ varPhi，\ varphi} \）正则性结果。