Lp-Sobolev regularity for integral operators over certain hypersurfaces

Ya-Ryong Heo; Sunggeum Hong; Chan Woo Yang

doi:10.4134/BKMS.2014.51.4.965

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

Ya-Ryong Heo, Sunggeum Hong, Chan Woo Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we establish sharp L^p-regularity estimates for averaging operators with convolution kernel associated to hypersurfaces in ℝ^d(d ≥ 2) of the form y → (y,γ(y)) where y ∈ ℝ^d-1 and γ(y) = Σ^d-1 _i=1±|y_i|^m _i with 2 ≤ m1 ≤ · · · ≤ m_d-1.

Original language	English
Pages (from-to)	965-978
Number of pages	14
Journal	Bulletin of the Korean Mathematical Society
Volume	51
Issue number	4
DOIs	https://doi.org/10.4134/BKMS.2014.51.4.965
Publication status	Published - 2014 Jan 1

ASJC Scopus subject areas

Mathematics(all)

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10.4134/BKMS.2014.51.4.965

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title = "Lp-Sobolev regularity for integral operators over certain hypersurfaces",

abstract = "In this paper we establish sharp Lp-regularity estimates for averaging operators with convolution kernel associated to hypersurfaces in ℝd(d ≥ 2) of the form y → (y,γ(y)) where y ∈ ℝd-1 and γ(y) = Σd-1 i=1±|yi|m i with 2 ≤ m1 ≤ · · · ≤ md-1.",

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AU - Hong, Sunggeum

AU - Yang, Chan Woo

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AB - In this paper we establish sharp Lp-regularity estimates for averaging operators with convolution kernel associated to hypersurfaces in ℝd(d ≥ 2) of the form y → (y,γ(y)) where y ∈ ℝd-1 and γ(y) = Σd-1 i=1±|yi|m i with 2 ≤ m1 ≤ · · · ≤ md-1.

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

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