数学与计算机科学 |
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一般齐次核Hardy-Mulholland型不等式 |
黄启亮, 杨必成, 王爱珍 |
广东第二师范学院 数学系,广东 广州 510303 |
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A Hardy-Mulholland-type inequality with the general homogeneous kernel |
HUANG Qiliang, YANG Bicheng, WANG Aizhen |
Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China |
1 HARDY G H, LITTLEWOOD J E, PÓLYA G. Inequalities[M]. Cambridge: Cambridge University Press, 1952: 255-292 . 2 MITRINOVIĆ D S, PIČARIĆ J E, FINK A M. Inequalities Involving Functions and Their Integrals and Derivatives[M]. Boston: Kluwer Academic Publishers, 1991.DOI:10.1007/978-94-011-3562-7_18 3 杨必成.算子范数与Hilbert型不等式[M].北京:科学 出版社,2009. YANG B C. The Norm of Operator and Hilbert-type Inequalities[M]. Beijing: Science Press, 2009. 4 YANG B C. Discrete Hilbert-Type Inequalities [M]. Sharjah : Bentham Science Publishers, 2011. 5 KRNIĆ M, GAO M Z, PEČARIĆ J, et al. On the best constant in Hilbert’s inequality [J]. Mathematical Inequalities and Applications, 2005, 8(2): 317-329. DOI:10.7153/mia-08-29 6 ČIŽMEŠIJA A, KRNIĆ M, PEČARIĆ J. General Hilbert-type inequalities with non-conjugate exponents[J]. Mathematical Inequalities and Applications, 2008, 11(2): 237-269.DOI:10.7153/mia-11-18 7 YANG B C, CHEN Q. On a Hardy-Hilbert-type inequality with parameters[J]. Journal of Inequalities and Applications, 2015(2015): 339.DOI:10.1186/s13660-015-0861-7 8 RASSIAS M TH, YANG B C. On a Hardy-Hilbert-type inequality with a general homogeneous kernel[J]. International Journal of Nonlinear Analysis and Applications, 2016,7(1): 249-269. 9 顾朝晖,杨必成. 一个加强的Hardy-Hilbert型不等式 [J]. 浙江大学学报(理学版), 2016, 43(5): 532-536. DOI:10.3785/j.issn.1008-9497.2016.05.006 GU Z H, YANG B C. A strengthened version of a Hardy-Hilbert-type inequality[J]. Journal of Zhejiang University (Science Edition), 2016, 43(5): 532-536. DOI:10.3785/j.issn.1008-9497.2016.05.006 10 洪勇,温雅敏. 齐次核的Hilbert型级数不等式取最佳 常数因子的充要条件[J]. 数学年刊 (A辑), 2016, 37(3): 329-336. HONG Y, WEN Y M. A necessary and sufficient condition of that Hilbert type series inequality with homogeneous kernel has the best constant factor[J]. Chinese Annals of Mathematics (Ser A), 2016, 37(3): 329-336. 11 洪勇. 具有齐次核的Hilbert型积分不等式的构造特 征及应用[J].吉林大学学报(理学版), 2017, 55(2): 189-194. DOI:10.13413/j.cnki.jdxblxb.2017.02.01 HONG Y. On the structure character of Hilbert's type integral inequality with homogeneous kernel and applications[J]. Journal of Jilin University (Science Edition), 2017, 55(2): 189-194. DOI:10.13413/j.cnki.jdxblxb.2017.02.01 12 HONG Y, HUANG Q L, YANG B C, et al. The necessary and sufficient conditions for the existence of a kind of Hilbert-type multiple integral inequality with the non-homogeneous kernel and its applications[J]. Journal of Inequalities and Applications ,2017(1):316-328. DOI:10.1186/s13660-017-1592-8 13 XIN D M, YANG B C, WANG A Z. Equivalent property of a Hilbert-type integral inequality related to the beta function in the whole plane[J]. Journal of Function Spaces, 2018:2691816. DOI:10.1155/2018/2691816 14 HONG Y, HE B, YANG B C. Necessary and sufficient conditions for the validity of Hilbert type integral inequalities with a class of quasi-homogeneous kernels and its application in operator theory[J]. Journal of Mathematics Inequalities, 2018, 12(3): 777 -788. DOI:10.7153/jmi-2018-12-59 15 HUANG Z X, YANG B C. Equivalent property of a half-discrete Hilbert’s inequality with parameters[J]. Journal of Inequalities and Applications, 2018(2018): 333. DOI:10.1186/s13660-018-1926-1 16 匡继昌.常用不等式[M].济南:山东科技出版社,2004. KUANG J C. Applied Inequalities[M]. Jinan: Shandong Science and Technology Press, 2004. 17 匡继昌.实分析与泛函分析(续论)(上册)[M]. 北京: 高等教育出版社, 2015. KUANG J C. Real Analysis and Functional Analysis (Continuation)(Volume one)[M]. Beijing: Higher Education Press, 2015. |
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