Some Generalisations and Refinements of the Hardy Inequality
Some recent results connected with the one-dimensional Hardy operator are given. Namely, some fractional order analogues of the classical Hardy inequality are discussed, and results concerning the two-dimensional Hardy operator are extended to Hardy operators defined on 1ℝ M × ℝ N . The main tools are the interpolation theory and some direct approaches for the fractional order case, and a recently derived N-dimensional Hardy inequality for operators on ℝ N .
Key words and phrasesHardy inequalities Fractional order derivatives Weighted Lebesgue spaces More-dimensional inequalities
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- 3.V. Burenkov and W. D. Evans, Weighted Hardy’s inequality for differences and the extension problem for spaces with generalized smoothness (to appear).Google Scholar
- 8.A. Kufner and L. E. Persson, Hardy inequalities of fractional order via interpolation, WS-SIAA (1994), 417-430.Google Scholar