$L^pL^q$ estimates for convolutions with distribution kernels having singularities on the light cone
Preprint Series # 684 Cho, Yonggeun and Kim, Youngcheol and Lee, Sanghyuk and Shim, Yongsun $L^pL^q$ estimates for convolutions with distribution kernels having singularities on the light cone. (2005); AbstractWe study the convolution operator $T^z$ with the distribution
kernel given by analytic continuation from the function
$$
\widetilde{K}^z(y,s,t)= \left\{\begin{array}{ll}
(t^2s^2y^2)_+^z/\Gamma(z+1)\quad &\mbox{if}\quad t>0\\
0 \quad&\mbox{if} \quad t\le 0\end{array}\right\}, \quad Re(z)>1
$$
where $(y,s,t)\in \mathbb R^{n1}\times\mathbb R\times \mathbb R$.
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
$\mathbb{R}^{n+1},\, n \ge 2$. Item Type:  Preprint 

Additional Information:  10copies 

Uncontrolled Keywords:  cone, convolution estimates 

Subjects:  42xx FOURIER ANALYSIS 

ID Code:  845 

