| Citation: |
ZENG Zhihong, YANG Bicheng. A Hardy-Hilbert-type Integral Inequality Involving the Derivative Functions of n-Order[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(4): 123-128. DOI: 10.6054/j.jscnun.2024058
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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.
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