构建一类非齐次核的Hilbert型积分不等式的等价参数条件 |
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引用本文: | 洪勇,陈强.构建一类非齐次核的Hilbert型积分不等式的等价参数条件[J].华南师范大学学报(自然科学版),2020,52(5):124-128. |
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作者姓名: | 洪勇 陈强 |
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作者单位: | 1.广东白云学院数学教研室,广州 510450 |
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摘 要: | 利用权函数方法,讨论了非齐次核K(x, y)=φλ(xλ1yλ2)φ′(xλ1yλ2)的Hilbert型积分不等式成立的等价参数条件及最佳常数因子,得到了构建此类Hilbert型不等式的充分必要条件及最佳常数因子的表达公式;对一些具体的非齐次核,得到了若干具有最佳常数因子的新的Hilbert型不等式; 最后,讨论了相应奇异积分算子的有界性及其范数.
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关 键 词: | 非齐次核 Hilbert型积分不等式 等价参数条件 有界算子 算子范数 |
收稿时间: | 2020-03-26 |
Equivalent Parameter Conditions for the Construction of Hilbert-type Integral Inequalities with a Class of Non-homogeneous Kernels |
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Institution: | 1.Department of Mathematics, Guangdong Baiyun University, Guangzhou 510450, China2.Department of Computer Science, Guangdong University of Education, Guangzhou 510303, China |
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Abstract: | Using the weight function methods, the equivalent parameter conditions for the validity of Hilbert-type integral inequalities with non-homogeneous kernel K(x, y)=φλ(xλ1yλ2)φ′(xλ1yλ2) and the best constant factor are discussed. The necessary and sufficient conditions for constructing such Hilbert-type inequalities and the formula for expressing the best constant factor are obtained. Many new Hilbert-type integral inequalities with some specific non-homogeneous kernels and the best constant factors are also obtained. Finally, the norm and boundedness of corresponding singular integral operators are discussed. |
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