We prove Besov regularity estimates for the solution of the Dirichlet problem involving the integral fractional Laplacian of order $s$ in bounded Lipschitz domains $\Omega$: \[ \|u\|_{\dot{B}^{s+r}_{2,\infty}(\Omega)} \le C \|f\|_{L^2(\Omega)} \quad r = \min\{s,1/2\}. \] This estimate is consistent with the regularity on smooth domains and shows that there is no loss of regularity due to Lipschitz boundaries. The proof uses elementary ingredients, such as the variational structure of the problem and the difference quotient technique.

翻译：我们证明,Besov定期估算是解决Drichlet问题的常规性办法,涉及在受约束的Lipschitz域内分块排列的单价,美元:=========================================================================================================================================================================================================================================================================================================正正正正正正正正正正正正正正正正正,===========================================================================================================================================================