  In this paper we consider weak Harnack inequality and H\"older regularity
estimates for symmetric $\alpha$-stable L\'evy process in $\mathbb{R}^d$,
$\alpha \in (0,2)$, $d\geq 2$. We consider a symmetric $\alpha$-stable L\'evy
process $X$ for which a spherical part $\mu$ of the L\'evy measure is a
spectral measure. In addition, we assume that $\mu$ is absolutely continuous
with respect to the uniform measure $\sigma$ on the sphere and impose certain
bounds on the corresponding density. Eventually, we show that the weak Harnack
inequality holds, which we apply to prove H\"older regularity results.
