$L^p$-Sobolev regularity for integral operators over certain hypersurfaces
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 965-978
Printed July 31, 2014
Yaryong Heo, Sunggeum Hong, and Chan Woo Yang
Korea University, Chosun University, Korea University
Abstract : In this paper we establish sharp $L^p$-regularity estimatesfor averaging operators with convolution kernel associated to hypersurfaces in $\mathbb{R}^d$($d \geq 2$) of the form $y \mapsto (y,\gamma(y))$ where $y\in \mathbb{R}^{d-1}$ and $\gamma(y) = \sum_{i=1}^{d-1} \pm |y_i|^{m_i}$ with $2 \leq m_1\leq \cdots \leq m_{d-1}$.
Keywords : $L^p$-Sobolev regularity
MSC numbers : Primary 42B20
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