We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend the previous result in [6] for unmixed $L_p$-estimates without weights.

中文翻译：

---

具有局部和非局部时间导数的抛物线方程的加权混合范数估计方法

当系数仅在时间变量中可测量时，我们为非发散形式的普通和时间分数式抛物线方程提供了加权混合范数估计和可解性的统一方法。在空间变量中，领先系数局部具有较小的平均振荡。我们的结果扩展了 [6] 中先前的结果，用于没有权重的未混合 $L_p$ 估计。