Maximal functions associated to a family of flat curves in lacunary directions

被引：0
|
作者：
Oh, Jeongtae [1 ]
Kim, Joonil [1 ]
机构：
[1] Yonsei Univ, Dept Math, Seoul 120749, South Korea
来源：
MATHEMATISCHE ZEITSCHRIFT | 2024年 / 306卷 / 03期
基金：
新加坡国家研究基金会;
关键词：
HILBERT-TRANSFORMS; CONVEX CURVES; OPERATORS;
D O I：
10.1007/s00209-024-03430-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Consider the maximal operator defined by M-gamma(a)(x1,x2)=supk is an element of Zsupr>012r integral r-r|f(x1-t,x2-ak gamma(t))|dt, where{(t,gamma(t))}is a convex curve anda=(ak)is a lacunary sequence. We observe that gamma ' doubling assumption does not imply to theLpboundedness ofMa gamma. However, underthe infinitesimally doubling condition on gamma ', we obtain theLpboundedness ofMa gamma for all1<p< infinity.
引用
收藏
页数：14
相关论文
共 50 条
12345