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$L^p-L^q$ estimates for convolutions with distribution kernels having singularities on the light cone

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83835

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
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

Submitter: 数学紀要登録作業用

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