A half-discrete Hilbert-type inequality with a non-homogeneous kernel
YANG Bicheng1, CHEN Qiang2
1. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China;
2. Department of Computer Science, Guangdong University of Education, Guangzhou 510303, China
Abstract：By introducing independent parameters and applying the method of weight functions and technique of real analysis, a half-discrete Hilbert-type inequality with a non-homogeneous kernel and a best possible constant factor is provided. The equivalent forms with the best possible constant factors are considered.
[1] HARDY G H. Note on a theorem of Hilbert concerning series of positive terms[J]. Proceedings London Math Soc,1925,23(2):Records of Proc xlv-xlvi.
[2] HARDY G H, LITTLEWOOD J E, POLYA G. Inequalities[M]. Cambridge: Cambridge University Press,1952.
[3] YANG B C. On best extensions of Hardy-Hilbert's inequality with two parameters[J]. Journal of Inequalities in Pure and Applied Mathematics,2005,6(3):Article No 81.
[4] 王竹溪,郭敦仁.特殊函数论[M].北京:科学出版社,1979. WANG Z X,GUO D R. Introduction of Particular Functions[M]. Beijing: Science Press,1979.
[5] 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.
[6] YANG B C. Discrete Hilbert-type Inequalities[M]. Sharjah: Bentham Science Publishers,2011.
[7] 杨必成.一个推广的Hardy-Hilbert型不等式[J].广东第二师范学院学报,2015,35(3):1-8. YANG B C. An extension of Hardy-Hilbert-type inequality[J]. Journal of Guangdong University of Education,2015,35(3):1-8.
[8] 杨必成,陈强.一个半离散含多参数的Hilbert型不等式[J].浙江大学学报:理学版,2012,39(6):623-626. YANG B C, CHEN Q. A half-discrete Hilbert-type inequality with multi-parameters[J]. Journal of Zhejiang University: Science Edition,2012,39(6):623-626.
[9] HUANG Q L, WANG A Z, YANG B C. A more accurate half-discrete Hilbert-type inequality with a general non-homogeneous kernel and operator expressions[J]. Mathematical Inequalities and Applications,2014,17(1):367-388.
[10] WANG A Z, YANG B C. A more accurate reverse half-discrete Hilbert-type inequality[J]. Journal of Inequalities and Applications,2015:85.DOI:10.1186/s13660-015-0613-8.
[11] YANG B C, DEBNATH L. Half-Discrete Hilbert-Type Inequalities[M]. Singapore: World Scientific Publishing Co Pte Ltd,2014.
[12] 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.
[13] 匡继昌.实变函数与泛函分析(续论)[M].北京:高等教育出版社,2015. KUANG J C. Real Functions and Functional Analysis (Continuous)[M]. Beijing: Higher Education Press,2015.
2017, Vol. 44 
