1 |
HARDY G H, LITTLEWOOD J E, PÖLYA G. Inequalities[M]. Cambridge: Cambridge University Press, 1952.
|
2 |
匡继昌. 常用不等式[M]. 济南: 山东科学技术出版社, 2004. KUANG J C. Applied Inequalities[M]. Jinan: Shandong Science and Technology Press, 2004.
|
3 |
YANG B C. A mixed Hilbert-type inequality with a best constant factor[J]. International Journal of Pure and Applied Mathematics, 2005, 20(3): 319-328.
|
4 |
BONSALL F F. Inequalities with non-conjugate parameter[J]. The Quarterly Journal of Mathematics, 1951, 2(2): 135-150. DOI:10.1093/qmath/2.1.135
doi: 10.1093/qmath/2.1.135
|
5 |
YANG B C. On a more accurate Hilbert's type inequality[J]. International Mathematical Forum, 2007, 2(37): 1831-1837. DOI:10.12988/imf.2007. 07162
doi: 10.12988/imf.2007. 07162
|
6 |
KUANG J C, DEBNATH L. On Hilbert's type inequalities on the weighted Orlicz spaces[J]. Pacific Journal of Applied Mathematics, 2007, 1(1): 95-103.
|
7 |
洪勇, 孔荫莹. 含变量可转移函数核的Hilbert型级数不等式[J]. 数学物理学报, 2014, 34A(3): 708-715. HONG Y, KONG Y Y. A Hilbert-type series inequality with transferable variable kernel[J]. Acta Mathematica Scientia, 2014, 34A(3): 708-715.
|
8 |
洪勇. 带对称齐次核的级数算子的范数刻画及其应用[J]. 数学学报, 2008, 51(2): 209-216. doi:10.3321/j.issn:0583-1431.2008.02.019 HONG Y. On the norm of a series operator with a symmetric and homogeneous kernel and its application[J]. Acta Mathematica Sinica, 2008, 51(2): 209-216. doi:10.3321/j.issn:0583-1431.2008.02.019
doi: 10.3321/j.issn:0583-1431.2008.02.019
|
9 |
洪勇. Hardy-Hilbert积分不等式的全方位推广[J]. 数学学报, 2001, 44(4): 619-626. doi:10.3321/j.issn:0583-1431.2001.04.007 HONG Y. All-sided generalization about Hardy-Hilbert integral inequalities[J]. Acta Mathematica Sinica, 2001, 44(4): 619-626. doi:10.3321/j.issn:0583-1431.2001.04.007
doi: 10.3321/j.issn:0583-1431.2001.04.007
|
10 |
KRNIĆ M, PEČARIĆ J, VUKOVIĆ P. On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters[J]. Mathematical Inequalities & Applications, 2008, 11: 701-716. DOI:10.7153/MIA-11-60
doi: 10.7153/MIA-11-60
|
11 |
RASSIAS M TH, YANG B C. A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function[J]. Applied Mathematics and Computation, 2013, 225: 263-277. DOI:10.1016/j.amc.2013.09.040
doi: 10.1016/j.amc.2013.09.040
|
12 |
RASSIAS M TH, YANG B C. On a Multidimensional half-discrete Hilbert-type inequality related to the hyperbolic cotangent function[J]. Applied Mathematics and Computation, 2014, 242: 800-813. DOI:10.1016/j.amc.2014.06.056
doi: 10.1016/j.amc.2014.06.056
|
13 |
ZHONG W Y, YANG B C. On a multiple Hilbert-type integral inequality with the symmetric kernel[J]. Journal of Inequalities and Applications, 2007: 27962. DOI:10.1155/2007/27962
doi: 10.1155/2007/27962
|
14 |
LIU T, YANG B C, HE L P. On a multidimensional Hilbert-type integral inequality with logarithm function[J]. Mathematical Inequalities and Applications, 2015, 18(4): 1219-1234. DOI:10. 7153/mia-18-94
doi: 10. 7153/mia-18-94
|
15 |
YANG B C. A multidimensional discrete Hilbert-type inequality[J]. International Journal of Nonlinear Analysis and Applications, 2014, 5(1): 80-88.
|
16 |
和炳, 曹俊飞, 杨必成. 一个全新的多重Hilbert型积分不等式[J]. 数学学报, 2015, 58(4): 661-672. HE B, CAO J F, YANG B C. A brand new multiple Hilbert-type integral inequality[J]. Acta Mathematics Sinica, 2015, 58(4): 661-672.
|
17 |
洪勇. 一类具有准齐次核的涉及多个函数的Hilbert型积分不等式[J]. 数学学报, 2014, 57(5): 833-840. HONG Y. A Hilbert-type integral inequality with quasi-homogeneous kernel and serveral functions[J]. Acta Mathematica Sinica, 2014, 57(5): 833-840.
|
18 |
洪勇. 一类带齐次核的奇异重积分算子的范数及其应用[J]. 数学年刊A辑(中文版), 2011, 32(5): 599-606. HONG Y. On the norm of singular multiple integral operator with homogeneous krenel and its application[J]. Chinese Annals of Mathematics (Ser A), 2011, 32(5): 599-606.
|
19 |
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(中文版), 2016, 37(3): 329-336. HONG Y, WEN Y M. A necessary and sufficient conditions 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.
|
20 |
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 Mathematical Inequalities, 2018, 12(3): 777-788. DOI:10.7153/jmi-2018-12-59
doi: 10.7153/jmi-2018-12-59
|
21 |
CAO J F, HE B, HONG Y, et al. Equivalent conditions and applications of a class of Hilbert-type integral inequalities involving multiple functions with quasi-homogeneous kernels[J]. Journal of Inequalities and Applications, 2018 (2018): 206. DOI:10.1186/s13660-018-1797-5
doi: 10.1186/s13660-018-1797-5
|
22 |
徐利治, 郭永康. 关于Hilbert不等式的Hardy-Riesz拓广的注记[J]. 数学季刊, 1991, 6(1): 75-77. XU L Z, GUO Y K. Note on Hardy-Riesz's extension of Hilbert's inequality[J]. Chinese Quarterly Journal of Mathematics, 1991, 6(1): 75-77.
|
23 |
FICHTINGOLOZ G M. 微积分教程[M]. 北京:人民教育出版社, 1957: 404-423. FICHTINGOLOZ G M. A Course in Differetial and Integral Calculus [M]. Beijing: People Education Press, 1957: 404-423.
|