$L^p$-Sobolev regularity for integral operators over certain hypersurfaces

Yaryong Heo; Sunggeum Hong; Chan Woo Yang

doi:10.4134/BKMS.2014.51.4.965

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(4): 965-978

Printed July 31, 2014

https://doi.org/10.4134/BKMS.2014.51.4.965

$L^p$-Sobolev regularity for integral operators over certain hypersurfaces

Yaryong Heo, Sunggeum Hong, and Chan Woo Yang

Korea University, Chosun University, Korea University

Abstract

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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