Ufa Mathematical Journal
    Volume 5, Number 2, pp. 43-55

    Hardy type inequalities with logarithmic and power weights for a special family of non-convex domains

    Nasibullin R.G., Tuhvatullina A.M.


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    In the present work we obtain variational Hardy type inequalities with power and logarithmic weights which are generalizations of the corresponding inequalities given earlier in the papers by M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev, and J. Tidblom. We formulate and prove inequalities for arbitrary domains, and then we substantially simplify them for the class of convex domains and a special family of non-convex domains.