关键词: Hilbert型积分不等式, 权函数, Whittaker函数, Hilbert型积分算子, 合流超几何函数

Abstract: By using the weight function method, the technique of the real analysis and the related theories of special functions, the author established a Hilberttype integral inequality with multiparameters related to some special functions and its equivalence, proved that its  constant factors were optimal, and  gave the operator expressions with the norm. 

Key words: Hilberttype integral inequality, weight function, Whittaker function, Hilberttype integral operator, confluent hypergeometric function