Regularity of the Fractional Maximal Function
Regularity of the Fractional Maximal Function
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DOI：
10.1112/s0024609303002017
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发表时间：
2003-07
影响因子：
0.9
通讯作者：
J. Kinnunen;E. Saksman
中科院分区：
文献类型：
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作者：
J. Kinnunen;E. Saksman
这项工作的目的是表明，分数极大算子有一些意想不到的规律性。主要结果表明，分数极大算子将Lp-空间有界映射到某些一阶Sobolev空间。还证明了分数极大算子保持一阶Sobolev空间。这推广了哈代‐Littlewood极大算子的已知结果. 2000年数学学科分类42 B25，46 E35。
The purpose of this work is to show that the fractional maximal operator has somewhat unexpected regularity properties. The main result shows that the fractional maximal operator maps Lp‐spaces boundedly into certain first‐order Sobolev spaces. It is also proved that the fractional maximal operator preserves first‐order Sobolev spaces. This extends known results for the Hardy‐Littlewood maximal operator. 2000 Mathematics Subject Classification 42B25, 46E35.