Multiple singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces
Multiple singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces
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沿表面具有混合同质性的多重奇异积分和 Marcinkiewicz 积分
DOI：
10.1186/1029-242x-2012-189
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发表时间：
2012-01-01
影响因子：
1.6
通讯作者：
Wu, Huoxiong
中科院分区：
文献类型：
--
作者：
Liu, Feng;Wu, Huoxiong
本文致力于研究乘积域 R-m x R-n (m, n >= 2) 上沿曲面的奇异积分和具有混合齐次性的 Marcinkiewicz 积分，其中包含许多经典曲面作为模型示例。在内核相当弱的尺寸条件下，建立了此类算子的 L-p(R-m x R-n) 有界性。这些结果本质上扩展了之前的某些结果。
This paper is devoted to studying the singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces, which contain many classical surfaces as model examples, on the product domains R-m x R-n (m, n >= 2). Under rather weak size conditions of the kernels, the L-p(R-m x R-n)-boundedness for such operators is established. These results essentially extend certain previous results.