Browse > Article
http://dx.doi.org/10.4134/BKMS.2014.51.4.965

Lp-SOBOLEV REGULARITY FOR INTEGRAL OPERATORS OVER CERTAIN HYPERSURFACES  

Heo, Yaryong (Department of Mathematics Korea University)
Hong, Sunggeum (Department of Mathematics Chosun University)
Yang, Chan Woo (Department of Mathematics Korea University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.4, 2014 , pp. 965-978 More about this Journal
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;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Christ, Failure of an endpoint estimate for integrals along curves, Fourier analysis and partial differential equations (Miraflores de la Sierra, 1992), 163-168, Stud. Adv. Math. CRC, Boca Raton, FL, 1995.
2 E. Ferreyra, T. Godoy, and M. Urciuolo, Endpoint bounds for convolution operators with singular measures, Colloq. Math. 76 (1998), no. 1, 35-47.   DOI
3 A. Iosevich, E. Sawyer, and A. Seeger, On averaging operators associated with convex hypersurfaces of finite type, J. Anal. Math. 79 (1999), 159-187.   DOI
4 A. Nagel, A. Seeger, and S. Wainger, Averages over convex hypersurfaces, Amer. J. Math. 115 (1993), no. 4, 903-927.   DOI   ScienceOn
5 A. Seeger, Some inequalities for singular convolution operators in Lp-spaces, Trans. Amer. Math. Soc. 308 (1988), no. 1, 259-272.
6 A. Seeger and T. Tao, Sharp Lorentz space estimates for rough operators, Math. Ann. 320 (2001), no. 2, 381-415.   DOI