On unboundedness of maximal operators for directional hilbert transforms

被引：22
|
作者：
Karagulyan, G. A. [1 ]
机构：
[1] Armenian Natl Acad Sci, Inst Math, Yerevan 375019, Armenia
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 135卷 / 10期
关键词：
hilbert transform; maximal function;
D O I：
10.1090/S0002-9939-07-08731-X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that for any infinite set of unit vectors U in R-2 the maximal operator defined by H(U)f(x) = sup u is an element of U vertical bar pv integral(infinity)(-infinity) f(x - tu)/t dt vertical bar, x is an element of R-2, is not bounded in L-2(R-2).
引用
收藏
页码：3133 / 3141
页数：9
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