Rough singular integrals on Triebel-Lizorkin space and Besov space
Rough singular integrals on Triebel-Lizorkin space and Besov space
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DOI：
10.1016/j.jmaa.2008.06.039
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发表时间：
2008-11
影响因子：
1.3
通讯作者：
Yanping Chen;Yong Ding
中科院分区：
文献类型：
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作者：
Yanping Chen;Yong Ding
证明了齐次奇异积分TΩ与Ω∈H1(SnBesorkin 1)在−空间和Besov空间上是有界的.这些结果回答了Chen和Zhang在[J.Chen，C.Zhang，Triebel-Lizorkin空间上粗糙奇异积分的有界性，J.Math]中提出的一个公开问题。肛门。APPL337(2008)1048-1052]。同样的结果也适用于具有径向函数核的粗糙奇异积分算子TΩ。
In this paper the authors prove that the homogeneous singular integral TΩwith Ω∈H1(Sn−1) is bounded on the Triebel–Lizorkin spaces and the Besov spaces. These results answer an open problem proposed by Chen and Zhang in [J. Chen, C. Zhang, Boundedness of rough singular integral on the Triebel–Lizorkin spaces, J. Math. Anal. Appl. 337 (2008) 1048–1052]. The same results hold also for the rough singular integral operators TΩ,hwith radial function kernels.