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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
Posted:
March 21, 2006
MathSciNet review:
2213710
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Additional Information
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.
References
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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
Posted:
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-$\Gamma$-01-108).
Communicated by:
Jonathan M. Borwein
Article copyright:
© Copyright 2006 American Mathematical Society
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