A new improvement of Hilbert's inequality for double series can be establishedby means of a strengthened Cauchy's inequality. As application, a quite sharp result onFejer-Riesz's inequality is obtained.
In this paper it is shown that a refinement on the weighted Hilbert inequalityfor double series can be established by introducing a proper non-zero real number R_ω.The expression of R_ω is given by means of the posi...In this paper it is shown that a refinement on the weighted Hilbert inequalityfor double series can be established by introducing a proper non-zero real number R_ω.The expression of R_ω is given by means of the positive definiteness of a Gram matrix.展开更多
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 sev...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.展开更多
文摘A new improvement of Hilbert's inequality for double series can be establishedby means of a strengthened Cauchy's inequality. As application, a quite sharp result onFejer-Riesz's inequality is obtained.
文摘In this paper it is shown that a refinement on the weighted Hilbert inequalityfor double series can be established by introducing a proper non-zero real number R_ω.The expression of R_ω is given by means of the positive definiteness of a Gram matrix.
文摘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.
