一个引入中间变量的一般非齐次核全平面Hilbert型积分不等式
On a Hilbert-Type Integral Inequality with the General Nonhomogeneous Kernel and the Intermediate Variables in the Whole Plane
应用实分析及权函数的方法,引入一些参数及中间变量,建立一个一般非齐次核全平面Hilbert型积分不等式的若干等价陈述.常数因子被证明是最佳的.作为应用,一个一般齐次核全平面Hilbert型积分不等式的若干等价陈述被导出.我们还考虑了一些特殊情况、算子表示及若干例子.
By means of the way of real analysis and the weight functions, introducing some parameters and intermediate variables, a few equivalent statements of a Hilberttype integral inequality with the general nonhomogeneous kernel in the whole plane are obtained. The constant factor is proved to be the best possible. As applications, a few equivalent statements of a Hilbert-type integral inequality with the general homogeneous kernel in the whole plane are deduced. We also consider some particular cases, the operator expressions and a few examples.
Hilbert型积分不等式 / 权函数 / 中间变量 / 等价形式 / 算子 {{custom_keyword}} /
Hilbert-type integral inequality / weight function / intermediate variable / equivalent form / operator {{custom_keyword}} /
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国家自然科学基金青年科学基金资助项目(11401113);广东省2017年重点平台及科研项目—特色创新类项目(自然科学)(2017KTSCX133)
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