Hardy type inequalities for a special family of non-convex domains

In this work, we obtain Hardy type inequalities that involve the distance to the boundary and the volume of a domain for a special family of non-convex domains. These inequalities are analogues of the inequalities for convex domains proved by M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev, and J. Tidblom. To prove Hardy type inequalities, we propose a sufficient condition of regularity for multidimensional domains. Hardy type inequalities for certain non-convex domains in two- and three-dimensional spaces are used as an example.