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Let $d \ge 2$. In this paper, we study weak solutions for the following typeof stochastic differential equation \[ dX_{t}=dS_{t}+b(s+t, X_{t})dt, \quadX_{0}=x, \] where $(s,x)\in \mathbb{R}_+ \times \mathbb{R}^{d}$ is the initialstarting point, $b: \mathbb{R}_+ \times \mathbb{R}^{d} \to \mathbb{R}^{d}$ ismeasurable, and $S=(S_{t})_{t \ge 0}$ is a $d$-dimensional $\alpha$-stableprocess with index $\alpha \in (1,2)$. We show that if the $\alpha$-stableprocess $S$ is non-degenerate and $b \inL_{loc}^{\infty}(\mathbb{R}_{+};L^{\infty}(\mathbb{R}^{d}))+L_{loc}^{q}(\mathbb{R}_{+};L^{p}(\mathbb{R}^{d}))$ for some $p,q>0$ with $d/p+\alpha/q <\alpha-1$, then the above SDE has a unique weak solution for everystarting point $(s,x)\in \mathbb{R}_+ \times \mathbb{R}^{d}$.

On Weak Solutions of SDEs with Singular Time-Dependent Drift and Driven by Stable Processes