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Lp-SOBOLEV REGULARITY FOR INTEGRAL OPERATORS OVER CERTAIN HYPERSURFACES

  • Received : 2013.06.26
  • Published : 2014.07.31

Abstract

In this paper we establish sharp $L^p$-regularity estimates for 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 ${\gamma}(y)={\sum}^{d-1}_{i=1}{\pm}{\mid}y_i{\mid}^{m_i}$ with $2{\leq}m_1{\leq}{\cdots}{\leq}m_{d-1}$.

Keywords

$L^p$-Sobolev regularity

References

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)