  Suppose that $d\geq1$ and $\alpha\in (1, 2)$. Let $Y$ be a rotationally
symmetric $\alpha$-stable process on $\R^d$ and $b$ a $\R^d$-valued measurable
function on $\R^d$ belonging to a certain Kato class of $Y$. We show that $\rd
X^b_t=\rd Y_t+b(X^b_t)\rd t$ with $X^b_0=x$ has a unique weak solution for
every $x\in \R^d$. Let $\sL^b=-(-\Delta)^{\alpha/2} + b \cdot \nabla$, which is
the infinitesimal generator of $X^b$. Denote by $C^\infty_c(\R^d)$ the space of
smooth functions on $\R^d$ with compact support. We further show that the
martingale problem for $(\sL^b, C^\infty_c(\R^d))$ has a unique solution for
each initial value $x\in \R^d$.
