Gao, Mingzhe; Yang, Bichen On the extended Hilbert’s inequality. (English) Zbl 0935.26011 Proc. Am. Math. Soc. 126, No. 3, 751-759 (1998). Hilbert’s inequality is well known. See, for example, G. H. Hardy, J. E. Littlewood and G. Pólya [“Inequalities” (1934; Zbl 0010.10703; 2nd ed. 1952; Zbl 0047.05302; reprint of the 2nd ed. 1988; Zbl 0634.26008)]. It has been extended from \(\ell_2\) norm to \(\ell_p\) norm. Also the corresponding inequality is sharp. The authors manage to bring the sharp constant inside the \(\ell_p\) and \(\ell_q\) norms where \(p>1\) and \(1/p+1/q=1\) and give a new version of Hilbert’s inequality involving sequences. See also M. Gao [J. Math. Anal. Appl. 212, No. 1, 316-323 (1997; Zbl 0890.26011)]. Reviewer: Lee Peng-Yee (Singapore) Cited in 1 ReviewCited in 53 Documents MSC: 26D15 Inequalities for sums, series and integrals Keywords:Hilbert inequality Citations:Zbl 0010.10703; Zbl 0047.05302; Zbl 0634.26008; Zbl 0890.26011 PDFBibTeX XMLCite \textit{M. Gao} and \textit{B. Yang}, Proc. Am. Math. Soc. 126, No. 3, 751--759 (1998; Zbl 0935.26011) Full Text: DOI References: [1] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, 1952. [2] D. S. Mitrinović, Analytic inequalities, Springer-Verlag, New York-Berlin, 1970. In cooperation with P. M. Vasić. Die Grundlehren der mathematischen Wissenschaften, Band 165. · Zbl 0199.38101 [3] Ming Zhe Gao, An improvement of the Hardy-Riesz extension of the Hilbert inequality, J. Math. Res. Exposition 14 (1994), no. 2, 255 – 259 (Chinese, with English and Chinese summaries). · Zbl 0816.26005 [4] Zhao Dejun, On a Refinement of Hilbert’s Double Series Theorem, Math. In Practice and Theory, Beijin, China. · Zbl 1135.42306 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.