关键词: Hilbert型积分不等式, 权函数, 核, 共轭指数

Abstract:

Introducing the weight function and using the way of real analysis, the author gave a new Hilberttype integral inequality with the homogeneous kernel of real numberdegree with three independent parameters and two pairs of conjugate exponents, which is a best extension of a Hilberttype integral inequality with the homogeneous kernel of 0-degree. The equivalent form, the reverses and some particular results were studied.

Key words: Hilberttype integral inequality, weight function, kernel, conjugate exponent