Singular integrals and multiplier operators
Singular integrals and multiplier operators
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DOI：
10.1007/bf02383650
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发表时间：
1971-12
期刊：
影响因子：
--
通讯作者：
N. Rivière
中科院分区：
文献类型：
--
作者：
N. Rivière
1952年，AP Calderon和A. Zygmund [6]证明了奇异积分算子在LP空间中的有界性。他们证明的主要工具之一是将F的一种形式推广到m维。Riesz's sun rising lemma.后来F. Jones [15]，EB Fabes和NM Rivi~ re [9]进一步推广了该引理，证明了抛物型奇异积分和混合齐次奇异积分的有界性。然而，在这两种情况下的引理保持其几何形式和它的扩展是通过一个简单的改变参数在每个坐标轴。
In 1952, AP Calderon and A. Zygmund [6] showed the boundedness of singular integral operators in the LP spaces. One of the main tools in their proof was an extension to m dimensions of a form of F. Riesz's sun rising lemma. Later F. Jones [15], and EB Fabes and NM Rivi~ re [9] further extended the lemma to prove the boundedness of parabolic singular integrals and singular integrals with mixed homogeneity. However in both cases the lemma kept its geometric form and its extension was obtained by a simple change of parameters in each coordinate axis.