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$L^p-L^q$ estimates for convolutions with distribution kernels having singularities on the light cone
Title: | $L^p-L^q$ estimates for convolutions with distribution kernels having singularities on the light cone |
Authors: | Cho, Yonggeun Browse this author | Kim, Youngcheol Browse this author | Lee, Sanghyuk Browse this author | Shim, Yongsun Browse this author |
Keywords: | cone | convolution estimates |
Issue Date: | 2005 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 684 |
Start Page: | 1 |
End Page: | 17 |
Abstract: | We study the convolution operator $T^z$ with the distribution kernel given by analytic continuation from the function $$ \widetilde{K}^z(y,s,t)= \left\{\begin{array}{ll} (t^2-s^2-|y|^2)_+^z/\Gamma(z+1)\quad &\mbox{if}\quad t>0\\ 0 \quad&\mbox{if} \quad t\le 0\end{array}\right\}, \quad Re(z)>-1 $$ where $(y,s,t)\in \mathbb R^{n-1}\times\mathbb R\times \mathbb R$. We obtain some improvement upon the previous known estimates for $T^z$. Then we extend the result of the cone multiplier of negative order on $\mathbb{R}^3$ \cite{lee1} to the case of general $\mathbb{R}^{n+1},\, n \ge 2$. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69489 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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