Lp-SOBOLEV REGULARITY FOR INTEGRAL OPERATORS OVER CERTAIN HYPERSURFACES

Title & Authors
Lp-SOBOLEV REGULARITY FOR INTEGRAL OPERATORS OVER CERTAIN HYPERSURFACES
Heo, Yaryong; Hong, Sunggeum; Yang, Chan Woo;

Abstract
In this paper we establish sharp $\small{L^p}$-regularity estimates for averaging operators with convolution kernel associated to hypersurfaces in $\small{\mathbb{R}^d(d{\geq}2)}$ of the form $\small{y{\mapsto}(y,{\gamma}(y))}$ where $\small{y{\in}\mathbb{R}^{d-1}}$ and $\small{{\gamma}(y)={\sum}^{d-1}_{i=1}{\pm}{\mid}y_i{\mid}^{m_i}}$ with $\small{2{\leq}m_1{\leq}{\cdots}{\leq}m_}$$\small{{d-1}}$.
Keywords
$\small{L^p}$-Sobolev regularity;
Language
English
Cited by
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