We prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polygons with analytic right-hand side. We localize the problem through the Caffarelli-Silvestre extension and study the tangential differentiability of the extended solutions, followed by bootstrapping based on Caccioppoli inequalities on dyadic decompositions of vertex, edge, and edge-vertex neighborhoods.

翻译：我们证明,在具有分析右侧的多边形中,对分层拉帕齐亚的分层拉帕齐亚(Drichlet)问题的解决方案具有加权分析性。 我们通过Caffarelli-Silvestre扩展来将问题本地化,并研究扩展解决方案的相近差异性,接着是基于Caccioppoli(Caccioppoli)不平等的靴子,在脊椎、边缘和边缘脊椎社区分解上进行分解。