On discrete fractional integral operators and related Diophantine equations

被引：3
|
作者：
Kim, Jongchon [1 ]
机构：
[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA
来源：
MATHEMATICAL RESEARCH LETTERS | 2015年 / 22卷 / 03期
基金：
美国国家科学基金会;
关键词：
MEAN-VALUE THEOREM;
D O I：
10.4310/MRL.2015.v22.n3.a11
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study discrete versions of fractional integral operators along curves and surfaces. l(p) -> l(q) estimates are obtained from upper bounds of the number of solutions of associated Diophantine systems. In particular, this relates the discrete fractional integral along the curve gamma(m) = (m, m(2), . . . , m(k)) to Vinogradov's mean value theorem. Sharp l(p) -> l(q) estimates of the discrete fractional integral along the hyperbolic paraboloid in Z(3) are also obtained except for endpoints.
引用
收藏
页码：841 / 857
页数：17
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