A Survey of Various Refinements and Generalizations of Hilbert's Inequalities  

Hilbert不等式的各种精化与拓广综述(英文)

作　　者：高明哲[1] 徐利治[2] 

机构地区：[1]吉首大学师范学院数学与计算机科学系,湖南吉首416000 [2]大连理工大学应用数学系,辽宁大连116024

出　　处：《Journal of Mathematical Research and Exposition》2005年第2期227-243,共17页数学研究与评论（英文版）

摘　　要：Expounded in this survey article is a series of refinements and generalizations of Hilbert's inequalities mostly published during the years 1990 through 2002.Those inequalities concerned may be classified into several types (discrete and integral etc.), and various related results obtained respectively by L. C. Hsu, M. Z. Gao, B. C. Yang, J. C. Kuang, Hu Ke and H. Hong et.al are described a little more precisely. Moreover, earlier and recent extensions of Hilbert-type inequalities are also stated for reference. And the new trend and the research ways are also brought forward.在本文中,我们较全面的概述了1990年至2002年间有关Hilbert级数型与积分型不等式的种种精化与拓广工作.涉及发表于海内外的文献资料40余篇,其中我国学者的工作成果占有重要份量.文末还列举了一些有待进一步研究的公开问题.

关 键 词：Hilbert's inequalities Hardy-Hilbert's inequalities weight function Gram matrix double series. 

分 类 号：O178[理学—数学]