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A note on Hardy-type inequalities
Author(s):
Peng
Gao
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1977-1984.
MSC (2000):
Primary 26D15, 26D20
Posted:
February 24, 2005
MathSciNet review:
2137863
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Abstract:
We use a theorem of Cartlidge and the technique of Redheffer's ``recurrent inequalities" to give some results on inequalities related to Hardy's inequality.
References:
-
- 1.
- H. Alzer, On Carleman's inequality, Portugal. Math., 50 (1993), 331-334. MR 1244510 (94j:26030)
- 2.
- G. Bennett, Some elementary inequalities, Quart. J. Math. Oxford Ser. (2), 38 (1987), 401-425. MR 0916225 (88k:26018)
- 3.
- G. Bennett, Some elementary inequalities, II, Quart. J. Math. Oxford Ser. (2), 39 (1988), 385-400. MR 0975904 (90a:26030)
- 4.
- G. Bennett, Some elementary inequalities, III, Quart. J. Math. Oxford Ser. (2), 42 (1991), 149-174. MR 1107279 (92h:26021)
- 5.
- G. Bennett, Factorizing the classical inequalities, Mem. Amer. Math. Soc., 120 (1996), 1-130. MR 1317938 (96h:26020)
- 6.
- G. Bennett, Inequalities complimentary to Hardy, Quart. J. Math. Oxford Ser. (2), 49 (1998), 395-432. MR 1652236 (2000a:26018)
- 7.
- G. Bennett and G. Jameson, Monotonic averages of convex functions, J. Math. Anal. Appl., 252 (2000), 410-430.MR 1797865 (2001k:26013)
- 8.
- J. M. Cartlidge, Weighted mean matrices as operators on
 , Ph.D. thesis, Indiana University, 1978. - 9.
- F. P. Cass and W. Kratz, Nörlund and weighted mean matrices as operators on
 , Rocky Mountain J. Math. 20 (1990), 59-74.MR 1057975 (91g:47024) - 10.
- G. H. Hardy, Orders of Infinity, Cambridge Univ. Press, 1954.MR 0349922 (50:2415)
- 11.
- G. H. Hardy, J.E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1952. MR 0046395 (13:727e)
- 12.
- V. I. Levin and S.B. Steckin, Inequalities, Amer. Math. Soc. Transl. (2), 14 (1960), 1-29. MR 0112925 (22:3771)
- 13.
- E. Love, Inequalities related to Carleman's inequality, Inequalities (Birmingham, 1987), 135-141, Lecture Notes in Pure and Applied Mathematics vol. 129, Dekker, New York, 1991.MR 1112576 (92i:26016)
- 14.
- J. Pecaric and K. Stolarsky, Carleman's inequality: history and new generalizations, Aequationes Math., 61 (2001), 49-62. MR 1820809 (2002m:26029)
- 15.
- R. M. Redheffer, Recurrent inequalities, Proc. London Math. Soc. (3), 17 (1967), 683-699. MR 0218513 (36:1599)
- 16.
- R. M. Redheffer, Easy proofs of hard inequalities, General inequalities 3 (ed. E. F. Beckenbach and W. Walter), 123-140, Birkhäuser Verlag, Basel, 1983. MR 0785770 (86i:26016)
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Additional Information:
Peng
Gao
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email:
penggao@umich.edu
DOI:
10.1090/S0002-9939-05-07964-5
PII:
S 0002-9939(05)07964-5
Keywords:
Hardy's inequality,
Carleman's inequality,
recurrent inequality
Received by editor(s):
June 20, 2003
Posted:
February 24, 2005
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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