Improved Hardy Inequalities with a Class of Weights

Anna Canale ()
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Anna Canale: Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy

Mathematics, 2023, vol. 11, issue 4, 1-11

Abstract: In the framework of Hardy type inequalities and their applications to evolution problems, the paper deals with local and nonlocal weighted improved Hardy inequalities related to the study of Kolmogorov operators perturbed by singular potentials. The class of weights is wide enough. We focus our attention on weighted Hardy inequalities with potentials obtained by inverse square potentials adding a nonnegative correction term. The method used to get the results is based on the introduction of a suitable vector-valued function and on a generalized vector field method. The local estimates show some examples of this type of potentials and extend some known results to the weighted case.

Keywords: improved Hardy inequality; weight functions; singular potentials; Kolmogorov operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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