A Hardy-Hilbert-type Integral Inequality Involving the Derivative Functions of n-Order

By means of the weight functions, the idea of introducing parameters and the method of real analysis, a new Hardy-Hilbert-type integral inequality with the homogeneous kernel as 1/(x+y)^λ+2n (λ >0) involving the derivative functions of n-order is established. The equivalent statements of the best possible constant factor related to several parameters are proved, and some particular (λ₁=λ/r, λ₂=λ/s (r>1, 1/r+1/s=1);λ=1, r=q, s=p) inequalities are gived.