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On inequalities of Hilbert's type

2007
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Bulletin of the Australian Mathematical Society
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By introducing the function l/(min{x,y}), we establish several new inequalities similar to Hilbert's type inequality. Moreover, some further unification of Hardy-Hilbert's and Hardy-Hilbert's type integral inequality and its equivalent form with the best constant factor are proved, which contain the classic Hilbert's inequality as special case. Jo then we have (see Hardy, Littlewood and Polya [4]) r Jo r ^Ĵ o Jo X + V Uo Jo where the constant factor •K is the best possible. Inequality (1.1) is

doi:10.1017/s0004972700039423
fatcat:gj2fsaxgdjhvrkbfgtcybnba54