On maximal functions with rough kernels in L(log L)1/2(Sn-1)
On maximal functions with rough kernels in L(log L)1/2(Sn-1)
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DOI：
10.1344/cm.v56i1.4069
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发表时间：
2005
影响因子：
1.1
通讯作者：
Ahmad Al-Salman
中科院分区：
文献类型：
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作者：
Ahmad Al-Salman
本文研究了与一类奇异积分算子相关的具有粗糙核的极大函数的Lp映射性质。我们证明了我们的极大函数是Lp上有界的，只要它们的核在L（log L）1/2（Sn-1）中。此外，我们提出了一个例子，表明我们的核的大小条件是最佳的。由于我们的结果，我们大大提高了以前已知的结果极大函数，奇异积分算子，参数Marcinkiewicz积分算子。
In this paper, we study the Lp mapping properties of maximal functions with rough kernels that are related to certain class of singular integral operators. We prove that our maximal functions are bounded on Lp provided that their kernels are in L(log L)1/2(Sn-1). Moreover, we present an example showing that our size condition on the kernel is optimal. As a consequence of our result, we substantially improve previously known results on maximal functions, singular integral operators, and Parametric Marcinkiewicz integral operators.