吴善和, 黄先勇, 杨必成. 一个涉及多重可变上限函数的半离散Hardy-Mulholland型不等式[J]. 华南师范大学学报(自然科学版), 2022, 54(1): 100-106. doi: 10.6054/j.jscnun.2022014
引用本文: 吴善和, 黄先勇, 杨必成. 一个涉及多重可变上限函数的半离散Hardy-Mulholland型不等式[J]. 华南师范大学学报(自然科学版), 2022, 54(1): 100-106. doi: 10.6054/j.jscnun.2022014
WU Shanhe, HUANG Xianyong, YANG Bicheng. A Half-discrete Hardy-Mulholland-type Inequality Involving One Multiple Upper Limit Function[J]. Journal of South China Normal University (Natural Science Edition), 2022, 54(1): 100-106. doi: 10.6054/j.jscnun.2022014
Citation: WU Shanhe, HUANG Xianyong, YANG Bicheng. A Half-discrete Hardy-Mulholland-type Inequality Involving One Multiple Upper Limit Function[J]. Journal of South China Normal University (Natural Science Edition), 2022, 54(1): 100-106. doi: 10.6054/j.jscnun.2022014

一个涉及多重可变上限函数的半离散Hardy-Mulholland型不等式

A Half-discrete Hardy-Mulholland-type Inequality Involving One Multiple Upper Limit Function

  • 摘要: 通过引入适当的核函数构造权函数,运用实分析技巧研究一类半离散Hardy-Mulholland型不等式:首先,建立一个涉及多参数和多重可变上限函数的半离散Hardy-Mulholland型不等式;然后,探讨该不等式的常数因子为最佳值时各参数之间的相关性及等价陈述,建立其等价不等式,刻画一类具有最佳常数因子的Hardy-Mulholland型不等式的结构特征。

     

    Abstract: By constructing the kernel function and weight function and using the real analytical techniques, the half-discrete inequalities of Hardy-Mulholland type are investigated. Firstly, a half-discrete Hardy-Mulholland-type inequality containing several parameters and one multiple upper limit function is established. And then, the equivalent statements on the best possible constant factor associated with several parameters are discussed with the aid of the proposed half-discrete Hardy-Mulholland-type inequality, and several inequalities are derived via their equivalent form. The results obtained can be used to depict the structure character of Hardy-Mulholland-type inequalities for which the constant factors are best possible.

     

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