We establish sharp regularity estimates for solutions to $Lu=f$ in $��\subset\mathbb R^n$, being $L$ the generator of any stable and symmetric L��vy process. Such nonlocal operators $L$ depend on a finite measure on $S^{n-1}$, called the spectral measure. First, we study the interior regularity of solutions to $Lu=f$ in $B_1$. We prove that if $f$ is $C^��$ then $u$ belong to $C^{��+2s}$ whenever $��+2s$ is not an integer. In case $f\in L^\infty$, we show that the solution $u$ is $C^{2s}$ when $s\neq1/2$, and $C^{2s-��}$ for all $��>0$ when $s=1/2$. Then, we study the boundary regularity of solutions to $Lu=f$ in $��$, $u=0$ in $\mathbb R^n\setminus��$, in $C^{1,1}$ domains $��$. We show that solutions $u$ satisfy $u/d^s\in C^{s-��}(\overline��)$ for all $��>0$, where $d$ is the distance to $\partial��$. Finally, we show that our results are sharp by constructing two counterexamples.

arXiv admin note: text overlap with arXiv:1404.1197