Some remarks on the restriction of the Fourier transform to surfaces
Some remarks on the restriction of the Fourier transform to surfaces
复制标题
关于傅里叶变换对曲面的限制的一些评论
DOI：
10.1017/s0305004100075848
复制
发表时间：
1993
影响因子：
0.8
通讯作者：
K. Guo
中科院分区：
文献类型：
--
作者：
S. Drury;K. Guo
对于一类核，我们证明了奇异Riesz势的Lp估计，并由此证明了Fourier变换对半维曲面的限制定理。给出了Brachio结果的一个简单证明.我们还发现，利用联合收割机的Hausdorff-Young定理和Februaryman-Zygmund方法证明约束定理的某些最优结果是可能的.
Abstract For a class of kernels, we prove the Lp estimate for the exotic Riesz potential, with which a restriction theorem of the Fourier transform to surfaces of half the ambient dimension is proved. A simpler proof of Barcelo's result is given. We also find that it is possible to combine the Hausdorff–Young theorem with the Fefferman–Zygmund method to prove some optimal results on the restriction theorem.