具有一般齐次核多维的半离散Hardy-Hilbert型不等式 黄启亮, 杨必成广东第二师范学院数学系 广州 广东 510303 An Extended Multidimensional Half-discrete Hardy-Hilbert-type Inequality with Homogeneous Kernel Qi Liang HUANG, Bi Cheng YANGDepartment of Mathematics, Guangdong University of Education, Guangzhou 510303, P. R. China

摘要 图/表 参考文献 相关文章 全文: PDF(522 KB) HTML (1 KB) 输出: BibTeX | EndNote (RIS) 摘要利用权函数、转换公式和实分析技巧，给出一个具有一般齐次核和最佳常数因子的多维半离散Hardy-Hilbert型不等式，它是一个已知结果的推广.此外，还讨论了等价形式、算子表示以及几种特殊应用例子. 服务 加入引用管理器 E-mail Alert RSS 收稿日期: 2019-07-17 MR (2010): O178 基金资助:国家自然科学基金资助项目（61772140）；广州市科技规划项目（201707010229） 通讯作者:杨必成E-mail: bcyang818@163.com 作者简介: 黄启亮,E-mail:qlhuang@yeah.net 引用本文: 黄启亮, 杨必成. 具有一般齐次核多维的半离散Hardy-Hilbert型不等式[J]. 数学学报, 2020, 63(5): 427-442. Qi Liang HUANG, Bi Cheng YANG. An Extended Multidimensional Half-discrete Hardy-Hilbert-type Inequality with Homogeneous Kernel. Acta Mathematica Sinica, Chinese Series, 2020, 63(5): 427-442. 链接本文: http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2020/V63/I5/427 [1] Azar L., On some extensions of Hardy-Hilbert's inequality and applications, Journal of Inequalities and Applications, 2008, No. 546829. 14pp. [2] Benyi A., Oh C. T., Best constant for certain multilinear integral operator, Journal of Inequalities and Applications, 2006, No. 28582. 12pp. [3] Hardy G. H., Littlewood J. E., Pólya G., Inequalities, Cambridge University Press, Cambridge, 1934. [4] Hong Y., On Hardy-Hilbert integral inequalities with some parameters, J. Inequal Pure Appl. Math., 2005, 6(4):Art. 92, 10pp. [5] Krni? M., Pe?ari? J. E., Hilbert's inequalities and their reverses, Publ. Math. Debrecen, 2005, 67(3-4):315-331. [6] Krni? M., Pe?ari? J. E., Vukovi? P., On some higher-dimensional Hilbert's and Hardy-Hilbert's type integral inequalities with parameters, Math. Inequal. Appl., 2008, 11:701-716. [7] Krni? M., Vukovi? P., On a multidimensional version of the Hilbert-type inequality, Analysis Mathematica, 2012, 38:291-303. [8] Kuang J. C., Applied Inequalities (in Chinese), Shangdong Science and Tech Press, Ji'nan, 2004. [9] Kuang J. C., Real and Functional Analysis (Continuation) (second volume), Higher Education Press, Beijing, 2015. [10] Kuang J. C., Debnath L., On Hilbert's type inequalities on the weighted Orlicz spaces, Pacific J. Appl. Math., 2007, 1(1):95-103. [11] Li Y. J., He B., On inequalities of Hilbert's type, Bulletin of the Australian Mathematical Society, 2007, 76(1):1-13. [12] Liu T., Yang B. C., He L. P., On a multidimensional Hilbert-type integral inequality with logarithm function, Mathematical Inequalities and Applications, 2015, 18(4):1219-1234. [13] Mitrinovi? D. S., Pe?ari? J. E., Fink A. M., Inequalities Involving Functions and their Integrals and Derivatives, Kluwer Academic Publishers, Boston, 1991. [14] Pan Y. L., Wang H. T., Wang F. T., On Complex Functions, Science Press, Beijing, 2006. [15] Rassias M. Th., Yang B. C., A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function, Applied Mathematics and Computation, 2013, 225:263-277. [16] Rassias M. Th., Yang B. C., On a multidimensional half-discrete Hilbert-type inequality related to the hyperbolic cotangent function, Applied Mathematics and Computation, 2014, 242:800-813. [17] Shi Y. P., Yang B. C., On a multidimensional Hilbert-type inequality with parameters, Journal of Inequalities and Applications, 2015, 2015:371. [18] Yang B. C., A mixed Hilbert-type inequality with a best constant factor, International Journal of Pure and Applied Mathematics, 2005, 20(3):319-328. [19] Yang B. C., A half-discrete Hilbert-type inequality, Journal of Guangdong University of Education, 2011, 31(3):1-7. [20] Yang B. C., A half-discrete Hilbert-type inequality with a non-homogeneous kernel and two variables, Mediterr. J. Math., 2013, 10:677-692. [21] Yang B. C., A multidimensional discrete Hilbert-type inequality, Int. J. Nonlinear Anal. Appl., 2014, 5(1):80-88. [22] Yang B. C., Discrete Hilbert-type Inequalities, Bentham Science Publishers Ltd., The United Areb Emirates, 2011. [23] Yang B. C., Hilbert-type Integral Inequalities, Bentham Science Publishers Ltd., The United Areb Emirates, 2009. [24] Yang B. C., Hilbert-type integral operators:Norms and Inequalities (In Chapter 42 of "Nonlinear Analysis, Stability, Approximation, and Inequalities" (P. M. Paralos et al.)), Springer, New York, 2012, 7:71-859. [25] Yang B. C., On Hilbert's Integral inequality, Journal of Mathematical Analysis and Applications, 1998, 220:778-785. [26] Yang B. C., The Norm of Operator and Hilbert-type Inequalities (in Chinese), Science Press, Beijing, 2009. [27] Yang B. C., Two Types of Multiple Half-discrete Hilbert-type Inequalities, Lambert Academic Publishing, Deutschland, 2012. [28] Yang B. C., Brneti? I, Krni? M., Pe?ari? J. E., Generalization of Hilbert and Hardy-Hilbert integral inequalities, Math. Ineq. Appl, 2005, 8(2):259-272. [29] Yang B. C., Chen Q., A half-discrete Hilbert-type inequality with a homogeneous kernel and an extension, Journal of Inequalities and Applications, 2011, 124, 16pp. [30] Yang B. C., Chen Q., A multidimensional discrete Hilbert-type inequality, Journal of Mathematical Inequalities, 2014, 8(2):267-277. [31] Yang B. C., Chen Q., On a Hardy-Hilbert-type inequality with parameters, Journal of Inequalities and Applications, 2015, 2015:339, 18pp. [32] Yang B. C., Debnath L., Half-discrete Hilbert-type Inequalities, World Scientific Publishing Co. Ptcc. Ltd., Singapore, 2014. [33] Yang B. C., Krni? M., On the norm of a mult-dimensional Hilbert-type operator, Sarajevo Journal of Mathematics, 2011, 7(20):223-243. [34] Yang B. C., Rassias Th. M., On the way of weight coefficient and research for Hilbert-type inequalities, Math. Ineq. Appl., 2003, 6(4):625-658. [35] Yang B. C., Rassias Th. M., On a Hilbert-type integral inequality in the subinterval and its operator expression, Banach J. Math. Anal., 2010, 4(2):100-110. [36] Zhong W. Y., A mixed Hilbert-type inequality and its equivalent forms, Journal of Guangdong University of Education, 2011, 31(5):18-22. [37] Zhong W. Y., A half discrete Hilbert-type inequality and its equivalent forms, Journal of Guangdong University of Education, 2012, 32(5):8-12. [38] Zhong W. Y., The Hilbert-type integral inequality with a homogeneous kernel of Lambda-degree, Journal of Inequalities and Applications, 2008, No. 917392, 12pp. [39] Zhong W. Y., Yang B. C., A best extension of Hilbert inequality involving several parameters, Journal of Jinan University (Natural Science), 2007, 28(1):20-23. [40] Zhong W. Y., Yang B. C., A reverse Hilbert's type integral inequality with some parameters and the equivalent forms, Pure and Applied Mathematics, 2008, 24(2):401-407. [41] Zhong J. H., Yang B. C., An extension of a multidimensional Hilbert-type inequality, Journal of Inequalities and Applications, 2017, 2017:78, 12pp. [42] Zhong W. Y., Yang B. C., On multiple Hardy-Hilbert's integral inequality with kernel, Journal of Inequalities and Applications, Vol. 2007, Art. ID 27962, 17pp. [43] Zhong J. H., Yang B. C., On an extension of a more accurate Hilbert-type inequality, Journal of Zhejiang University (Science Edition), 2008, 35(2):121-124. [1] 金建军. 若干新的p进制Hardy-Littlewood-Pólya型不等式[J]. 数学学报, 2020, 63(6): 639-646. [2] 何尚琴, 冯秀芳. 二维Helmholtz方程不适定问题的一种算子软化正则法[J]. 数学学报, 2020, 63(6): 545-556. [3] 李午栋, 张颖, 贺衎. 一类基于量子程序理论的序列效应代数[J]. 数学学报, 2020, 63(6): 647-654. [4] 林海波, 王宸雁. 非齐型空间上分数型Marcinkiewicz积分算子的加权估计[J]. 数学学报, 2020, 63(5): 443-464. [5] 王海蒙, 周璇, 赵玉娟. 四元Heisenberg群上次拉普拉斯算子的m幂次的基本解[J]. 数学学报, 2020, 63(3): 229-244. [6] 廖建全, 杨必成. 一个引入中间变量的一般非齐次核全平面Hilbert型积分不等式[J]. 数学学报, 2020, 63(1): 27-44. [7] 吴秀峰, 黄俊杰. 3×3阶上三角算子矩阵的点谱、剩余谱和连续谱[J]. 数学学报, 2019, 62(6): 817-832. [8] 刘永宏, 王为娜. Brown运动增量在Hölder范数下的局部泛函Chung重对数律[J]. 数学学报, 2019, 62(4): 605-612. [9] 王晓峰, 夏锦, 陈建军. 广义Fock空间上的Hankel算子[J]. 数学学报, 2019, 62(4): 561-572. [10] 乔艳芬, 侯国林, 阿拉坦仓. 基于二次算子族的无界Hamilton算子根向量组的基性质[J]. 数学学报, 2019, 62(4): 613-632. [11] 王晓峰, 夏锦, 陈建军. 广义Segal-Bargmann空间上无界Toeplitz算子的交换[J]. 数学学报, 2019, 62(3): 409-426. [12] 秦杰, 刘柚岐, 黄穗. Dirichlet空间上Bergman型Toeplitz算子的代数性质[J]. 数学学报, 2019, 62(3): 449-456. [13] 黄永峰, 曹怀信, 王文华. 伪自伴量子系统的酉演化与绝热定理[J]. 数学学报, 2019, 62(3): 469-478. [14] 杨沿奇, 陶双平. θ型C-Z算子在加权变指数Morrey空间上的有界性[J]. 数学学报, 2019, 62(3): 503-514. [15] 程旺, 马涛. 奇异积分算子q-变差的定量最优加权估计[J]. 数学学报, 2019, 62(2): 279-286. 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