Sharp one-weight and two-weight bounds for maximal operators

被引:23
作者
Moen, Kabe [1 ]
机构
[1] Univ Kansas, Lawrence, KS 66045 USA
基金
美国国家科学基金会;
关键词
maximal functions; weights; NORM INEQUALITIES; INTEGRALS;
D O I
10.4064/sm194-2-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We investigate the boundedness of,the fractional maximal operator with respect to a general basis on weighted Lebesgue spaces. We characterize the boundedness of these operators for one-weight and two-weight inequalities extending the work of Jawerth. A new two-weight testing condition for the fractional maximal operator on a general basis is introduced extending the work of Sawyer for the basis of cubes. We also find the sharp dependence in the two-weight case between the operator norm and the testing condition of Sawyer. Finally, our approach leads to a new proof of Buckley's sharp estimate for the Hardy-Littlewood maximal function.
引用
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页码:163 / 180
页数:18
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