一个实齐次核的Hilbert型积分不等式

A Hilbert-type Integral Inequality with Homogeneous Kernel of Real Number-degree

通过引入权函数,应用实分析的方法,建立一个具有3个独立参数及两对共轭指数的实齐次核的Hilbert型积分不等式,并研究了其等价形式、逆式及一些特殊结果,所给的不等式是一个零次齐次核的Hilbert型积分不等式的最佳推广.

Introducing the weight function and using the way of real analysis, the author gave a new Hilberttype 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 O-degree. The equivalent form, the reverses and some particular results were studied.