An $L_q(L_p)$-theory for diffusion equations with space-time nonlocal operators

Kyeong-hun Kim, Daehan Park, Junhee Ryu

We present an $L_q(L_p)$-theory for the equation $${\partial }_t^{\alpha }u=\varphi (\Delta )u+f,t>0,x\in {\mathbb{R}}^d;u(0,\cdot )=u_0.$$ Here $p,q>1$, $\alpha \in (0,1)$, $\partial…