Weighted inequalities and Stein-Weiss potentials

被引:58
作者
Beckner, William [1 ]
机构
[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA
关键词
D O I
10.1515/FORUM.2008.030
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Sharp extensions of Pitt's inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include Hardy-Rellich inequalities.
引用
收藏
页码:587 / 606
页数:20
相关论文
共 17 条
[1]   On a class of Rellich inequalities [J].
Barbatis, G ;
Tertikas, A .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 194 (01) :156-172
[2]   PITTS INEQUALITY AND THE UNCERTAINTY PRINCIPLE [J].
BECKNER, W .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (06) :1897-1905
[3]   Sharp inequalities and geometry manifolds [J].
Beckner, W .
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1997, 3 (Suppl 1) :825-836
[4]  
Beckner W., 1995, Essays on Fourier Analysis in Honour of Elias M. Stein, P36
[5]  
Brascamp H.J., 1974, J FUNCT ANAL, V17, P227, DOI [10.1016/0022-1236(74)90013-5, DOI 10.1016/0022-1236(74)90013-5]
[6]  
Chechkin A., 1960, Harmonic Analysis and the Theory of Probability
[7]   On weighted fractional integral inequalities [J].
Eilertsen, S .
JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 185 (01) :342-366
[8]   The uncertainty principle: A mathematical survey [J].
Folland, GB ;
Sitaram, A .
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1997, 3 (03) :207-238
[9]  
Hardy G.H., 1952, Inequalities
[10]  
Pitt H. R, 1937, DUKE MATH J, V3, P747