Study of singular integrals of variable type

对于与{x=Ψ（|y|）}曲面相关的变量核奇异积分，我们给出了与卷积核情况下相同的结果，当核为奇数时，当核为偶数时，在p=2附近的Lp有界性。对于更一般的内核情况，我们无法获得预期的结果。但是，在卷积型核的情况下，我们发表了7个关于粗糙核奇异积分、向量空间值奇异积分和多线性奇异积分的结果。这些都有助于奇异积分研究的发展。

For singular integrals with variable kernel associated to the surface of the form {x=Ψ(|y|)}, we showed the same result as in the convolution kernel case when the kernel is odd, and Lp boundedness near p=2 when the kernel is even. We could not achieve expected results for more general kernel cases. But, in the case of convolution type kernel, we published 7 results for singular integrals with rough kernel, vector space valued singular integrals and multilinear singular integrals. These contribute to the development of the study of singular integrals.