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Revista Colombiana de Matemáticas
versión impresa ISSN 0034-7426
Rev.colomb.mat. v.44 n.2 Bogotá jul./dic. 2010
1Universidad Nacional de Colombia, Bogotá, Colombia. Email: recastillo@unal.edu.co
2Universidad de Oriente, Cumaná, Venezuela. Email: eddycharles2007@hotmail.com
In this paper we make some further generalization of well known Hilbert's inequality and its equivalent form in two dimensional case. Many other results of this type in recent years follows as a special case of our results.
Key words: Hardy-Hilbert's inequality, Best constant, Hölder's inequality, Minkowski's integral inequality.
2000 Mathematics Subject Classification: 26D15.
En este artículo se hace una generalización de la conocida desigualdad de Hilbert y su forma equivalente en el caso de dos dimensiones. Otros resultados de este tipo de años recientes, se siguen como un caso especial de los resultados aquí presentados.
Palabras clave: Desigualdad de Hardy-Hilbert, mejor constante, desigualdad de Hölder, desigualdad integral de Minkowski.
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References
[1] Y. C. Chow, `On Inequalities of Hilbert and Widder´, J. London Math. Sco. 14, (1939), 151-154. [ Links ]
[2] G. B. Folland, Real Analysis. Modern Techniques, John Wiley and Sons, New York, United States, 1984. [ Links ]
[3] G. Hardy, `Note on a Theorem of Hilbert´, MathZ 6, (1920), 314-317. [ Links ]
[4] G. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge, United Kingdom, 1934. [ Links ]
[5] B. He, Y. Li, and Y. Qian, `On Analogues of the Hilbert's Inequality´, Communications in Mathematical Analysis 4, 2 (2008), 47-53. [ Links ]
[6] J. Knang, `On new Extensions of Hilbert's Integral Inequality´, Math. anal. appl 235, (1999), 608-614. [ Links ]
[7] Y. Li, J. Wu, and B. He, `A new Hilbert-Type Integral Inequality and the Equivalent Form´, International Journal of Mathematics and Mathematical Sciences vol. 2006, (2006), 1-6. Article ID 45378 [ Links ]
[8] B. G. Pachatte, `Inequalities Similar to the Integral Analogue of Hilbert's Inequality´, Tamkang J. Math 30, (1999), 139-146. [ Links ]
[9] B. Yang, `On the Norm of an Integral Operator and Applications´, J. Math. Anal. Appl 321, (2006), 182-192. [ Links ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv44n2a04,
AUTHOR = {Erlin Castillo, René and Trousselot, Eduard},
TITLE = {{Generalization of Hilbert's Integral Inequality}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2010},
volume = {44},
number = {2},
pages = {113-118}
}