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Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions |
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| Authors: | L.-E. Persson V. D. Stepanov E. P. Ushakova |
| Affiliation: | Department of Mathematics, Lulea University of Technology, SE-97187 Lulea, Sweden ; Department of Mathematical Analysis, Peoples Friendship University of Russia, Miklukho-Maklay 6, Moscow, 117198, Russia ; Computer Center of FEB RAS, Tikhookeanskaya 153, Khabarovsk, 680042, Russia |
| Abstract: | Some Hardy-type integral inequalities in general measure spaces, where the corresponding Hardy operator is replaced by a more general Volterra type integral operator with kernel  , are considered. The equivalence of such inequalities on the cones of non-negative respective non-increasing functions are established and applied. |
| Keywords: | Integral operator of the Hardy type inequalities for monotone functions |
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