On Multiple Hardy-hilbert Integral Inequalities with Some Parameters

where the constant factor [π/ sin(π/p)]p is also the best possible. Hardy-Hilbert inequalities are important in analysis and in their applications (see [7]). In recent years, many results (see [1, 3, 8–10]) have been obtained in the research of Hardy-Hilbert inequality. At present, because of the requirement of higher-dimensional harmonic analysis and higher-dimensional operator theory, multiple Hardy-Hilbert integral inequalities are researched (see [5, 6, 11]). Yang [11] obtains the following: if α ∈ R, n ≥ 2, pi > 1 (i= 1,2, . . . ,n), ∑n i=1(1/pi)= 1, λ > n−min1≤i≤n{pi}, fi ≥ 0, and