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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions


Authors: L.-E. Persson, V. D. Stepanov and E. P. Ushakova
Journal: Proc. Amer. Math. Soc. 134 (2006), 2363-2372
MSC (2000): Primary 26D15; Secondary 47B38
Published electronically: March 21, 2006
MathSciNet review: 2213710
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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 $ k(x,y)$, are considered. The equivalence of such inequalities on the cones of non-negative respective non-increasing functions are established and applied.


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Additional Information

L.-E. Persson
Affiliation: Department of Mathematics, Lulea University of Technology, SE-97187 Lulea, Sweden
Email: larserik@sm.luth.se

V. D. Stepanov
Affiliation: Department of Mathematical Analysis, Peoples Friendship University of Russia, Miklukho-Maklay 6, Moscow, 117198, Russia
Email: vstepanov@sci.pfu.edu.ru

E. P. Ushakova
Affiliation: Computer Center of FEB RAS, Tikhookeanskaya 153, Khabarovsk, 680042, Russia
Email: ushakova@as.khb.ru

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08403-6
PII: S 0002-9939(06)08403-6
Keywords: Integral operator of the Hardy type, inequalities for monotone functions
Received by editor(s): March 9, 2005
Published electronically: March 21, 2006
Additional Notes: The work of the second and third authors was financially supported by the Russian Foundation for Basic Researches (Projects 03–01–00017 and 05-01-00422) and by the Far-Eastern Branch of the Russian Academy of Sciences (Projects 05-III-A-01-12 and 05-III-$Γ$-01-108).
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society