Hong-Jie Dong

Weighted mixed-norm estimates for fractional parabolic equations with space-time nonlocal operators

We establish weighted mixed-norm estimates for fractional parabolic equations \begin{equation*} \partial_t^\alpha u=Lu-\lambda u+f \text{ in } (0,T)\times\mathbb{R}^d, \end{equation*} with nonlocal operators in both time and space. Here, $\partial_t^\alpha$ is the Caputo derivative of order $\alpha\in(0,1)$, and $L$ is...