Hilbert不等式的各种精化与拓广综述(英文)

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

中文关键词:  Hilbert不等式  Hardy-Hilbert不等式  权函数  Gram矩阵  重级数

英文关键词:Hilbert's inequalities  Hardy-Hilbert's inequalities  weight function  Gram matrix  double series.

中文摘要:

      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.

英文摘要:

      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.