A Sharp Weighted Wirtinger Inequality and Some Related Functional Spaces (Report‪)‬

1 Introduction and main results Wirtinger type inequalities are of interest in various areas of analysis and mathematical physics, including the Wulff theorem [3], quasiconformal mapping theory [8], p-Laplacian systems [11]. In view of their applications, they received a considerable attention in recent years. See, e.g., [1, 2, 4, 9,14] and the references therein.