Sharp Hardy inequalities of fractional order involving slowly varying functions |
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| Authors: | Petr Gurka Bohumír Opic |
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| Institution: | 1. Department of Mathematics, Czech University of Life Sciences Prague, 165 21 Prague 6, Czech Republic;2. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic |
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| Abstract: | We establish necessary and sufficient conditions for the validity of Hardy inequalities of fractional orders involving weights which are products of power-type functions and slowly varying functions. Consequently, for such weights, we solve Open Problems 1 and 2 mentioned in the book of Kufner and Persson, Weighted Inequalities of Hardy Type (World Scientific Publishing, 2003). |
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