一类非齐次核半离散 Hilbert型逆向不等式的构造定理及算子表示

A Construction Theorem and Operator Representation for Semi-discrete Hilbert-Type Reverse Inequality with Non-homogeneous Kernel

摘要

利用权系数方法和实分析技巧,考虑一类非齐次核的半离散 Hilbert型逆向不等式的构造,给出该类不等式的构造条件和最佳常数因子的计算公式,并给出不等式的算子表示及一些特例.

Abstract

Using the weight coefficient method and real analysis techniques, the author considers the constructing semi-discrete Hilbert-type reverse inequality with non-homogeneous kernel. It provides sufficient necessary conditions for constructing such inequality and calculation formulas for the best constant factor. Finally, the operator expression for the inequalities and some special cases are presented.

关键词

半离散 Hilbert型逆向不等式 / 非齐次核 / 构造定理 / 最佳常数因子 / 积分算子 / 离散算子

Key words

semi-discrete Hilbert-type reverse inequality / non-homogeneous kernel / construction theorem / the best constant factor / integral operator / discrete operator

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基金资助

广东省基础与应用基础研究基金(2022A1515012429)