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Linear and Multilinear Algebra Volume 67, 2019 - Issue 12
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Articles

Sharp norm estimates for a class of integral operators

Dah-Chin LuorDepartment of Financial and Computational Mathematics, I-Shou University, Kaohsiung City, TaiwanCorrespondence[email protected] [email protected]
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Pages 2504-2519 | Received 29 Jan 2018, Accepted 12 Jun 2018, Published online: 20 Jul 2018

References

  • Hardy GH, Littlewood JE, Pólya G. Inequalities. 2nd ed. Cambridge: Cambridge University Press; 1967.
  • Hardy GH. An inequality for Hausdorff means. J London Math Soc. 1943;18:46–50. doi: 10.1112/jlms/s1-18.1.46
  • Bennett G. Some elementary inequalities. Quart J Math Oxford. 1987;38:401–425. doi: 10.1093/qmath/38.4.401
  • Bennett G. Some elementary inequalities II. Quart J Math Oxford. 1988;39:385–400. doi: 10.1093/qmath/39.4.385
  • Bennett G. Some elementary inequalities III. Quart J Math Oxford. 1991;42:149–174. doi: 10.1093/qmath/42.1.149
  • Borwein D, Cass FP. Nörlund matrices as bounded operators on lp. Arch Math. 1984;42:464–469. doi: 10.1007/BF01190697
  • Bennett G. Inequalities complimentary to Hardy. Quart J Math Oxford. 1998;49:395–432. doi: 10.1093/qmathj/49.4.395
  • Chen C-P, Luor D-C, Ou Z-Y. Extensions of Hardy inequality. J Math Anal Appl. 2002;273:160–171. doi: 10.1016/S0022-247X(02)00232-9
  • Gao P. On lp norms of weighted mean matrices. Math Z. 2010;264:829–848. doi: 10.1007/s00209-009-0490-2
  • Gao P. Extensions of Copson's inequalities. J Math Anal Appl. 2013;401:430–435. doi: 10.1016/j.jmaa.2012.12.039
  • Chen C-P, Lan J-W, Luor D-C. The best constants for multidimensional modular inequalities over spherical cones. Linear Multilinear Algebra. 2014;62:683–713. doi: 10.1080/03081087.2013.777438
  • Chen C-P, Luor D-C. The weighted norm inequalities of integral operators with special types of kernels. Linear Multilinear Algebra. 2017;65:1734–1742. doi: 10.1080/03081087.2016.1254144
  • Copson ET. Some integral inequalities. Proc Roy Soc Edinb Sect A. 1975/1976;75:157–164. doi: 10.1017/S0308210500017868
  • Howard R, Schep AR. Norms of positive operators on Lp-spaces. Proc Amer Math Soc. 1990;109:135–146.
  • Love ER. Generalizations of Hardy's integral inequality. Proc Roy Soc Edinb Sect A. 1985;100:237–262. doi: 10.1017/S0308210500013792
  • Lu S, Yan D, Zhao F. Sharp bounds for Hardy type operators on higher-dimensional product spaces. J Inequal Appl. 2013;2013:148. DOI:10.1186/1029-242X-2013-148.
  • Sinnamon G. Schur's lemma and best constants in weighted norm inequalities. Le Matematiche. 2002;57:185–204.
  • Johnson Jr. PD, Mohapatra RN, Ross D. Bounds for the operator norms of some Nörlund matrices. Proc Amer Math Soc. 1996;124:543–547. doi: 10.1090/S0002-9939-96-03081-X
  • Bennett G, Grosse-Erdmann K-G. Weighted Hardy inequalities for decreasing sequences and functions. Math Ann. 2006;334:489–531. doi: 10.1007/s00208-005-0678-7
  • Mitrinovic DS, Vasic PM. History, variations and generalisations of the Čebyšev inequality and the question of some priorities. Univ Beograd Publ Elektrotehn Fak Ser Mat Fiz No. 1974;461–497:1–30.
  • Hewitt E, Stromberg K. Real and abstract analysis. Berlin: Springer-Verlag; 1965.
  • Borwein D. Simple conditions for matrices to be bounded operators on lp. Canad Math Bull. 1998;41:10–14. doi: 10.4153/CMB-1998-002-7

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