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On the extended Hilbert’s inequality. (English) Zbl 0935.26011
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 2 norm to p norm. Also the corresponding inequality is sharp. The authors manage to bring the sharp constant inside the p and 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)].

26D15Inequalities for sums, series and integrals of real functions