Abstract
A generalized Hardy-Hilbert inequality with weight function of the form B p−2+λ p , q−2+λ q �θr(λ)/(2n+1) λ − 2�λ r (with θr(λ) > 0,r = p, q ,1 � q 1) can be established by means of Euler-Maclaurin summation formula, where B(m,n) is β function. Inparticular, when λ = 1 ,animprovementonHardy-Hilbert'sinequality is obtained. As its applications, Hardy-Littlewood's inequality is extended and refined.
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