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Let Gðu, vÞ be a homogeneous nonnegative function of order λ, Kðn, kxkm,ρÞ =Gðnλ1 , kxk2 m,ρÞ. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality Ð R+ ∑n=1 Kðn, kxkm,ρÞan f ðxÞdx ≤Mk~akp,αk f kq,β are discussed. Finally, its applications in operator theory are discussed.

Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel