数学与计算机科学 |
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一个非单调非齐次核的Hilbert型积分不等式 |
钟建华1, 陈强2, 曾志红3 |
1. 广东第二师范学院 数学系, 广东 广州 510303; 2. 广东第二师范学院 计算机科学系, 广东 广州 510303; 3. 广东第二师范学院 学报编辑部, 广东 广州 510303 |
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A Hilbert-type integral inequality with a non-monotone and non-homogeneous kernel |
ZHONG Jianhua1, CHEN Qiang2, ZENG Zhihong3 |
1. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China; 2. Department of Computer Science, Guangdong University of Education, Guangzhou 510303, China; 3. Editorial Department of Journal, Guangdong University of Education, Guangzhou 510303, China |
[1] HARDY G H. Note on a theorem of Hilbert concerning series of positive term[J]. Proceeding of the London Math Society,1925,23(2):45-46. [2] HARDY G H,LITTLEWOOD J E,POLYE G. Inequalities[M]. Cambridge:Cambridge Univ Press,1952. [3] MINTRINOVIC D S,PECARIC J E,FINK A M. Inequalities Involving Functions and Their Integrals and Derivatives[M]. Boston:Kluwer Academic Publishers,1991. [4] YANG B C. On an extension of Hilbert's inequality with some parameters[J]. The Australian Journal of Mathematical Analysis and Applications,2004,1(1):1-8. [5] 杨必成.算子范数与Hilbert型不等式[M].北京:科学出版社,2009:300-307. YANG B C. The Norm of Operator and Hilbert-type Inequalities[M]. Beijing:The Science Press,2009:300-307. [6] 杨必成.关于一个非齐次核的Hilbert型积分算子[J].应用泛函分析学报, 2012,14(1):84-88. YANG B C. On a Hilbert-type integral operator with the none-homogeneous kernels[J]. Acta Analysis Functionalis Applicata,2012,14(1):84-88. [7] 钟玉泉.复变函数论[M].北京:高等教育出版社,2003. ZHONG Y Q. Theory of Functions of Complex Variable[M]. Beijing:Higher Education Press,2003. [8] 匡继昌.常用不等式[M].济南:山东科学技术出版社,2004:4-5. KUANG J C. Applied Inequalities[M]. Jinan:Shandong Science and Technology Press, 2004:4-5. [9] 匡继昌.实分析引论[M].长沙:湖南教育出版社,1996:45-46. KUANG J C. Real Analysis[M]. Changsha:Hunan Educational Press,1996:45-46. |
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