Maximal averages over certain non-smooth and non-convex hypersurfaces

Yaryong Heo; Sunggeum Hong; Chan Woo Yang

doi:10.11650/tjm/180204

Maximal averages over certain non-smooth and non-convex hypersurfaces

Yaryong Heo, Sunggeum Hong, Chan Woo Yang

Department of Mathematics

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

Abstract

We consider the maximal operators whose averages are taken over some non-smooth and non-convex hypersurfaces. For each 1 ≤ i ≤ d−1, let φ_i: [−1,1] → R be a continuous function satisfying some derivative conditions, and let (Formula presented). We prove the L^p boundedness of the maximal operators associated with the graph of φ which is a non-smooth and non-convex hypersurface in R^d, d ≥ 3.

Original language	English
Pages (from-to)	1383-1401
Number of pages	19
Journal	Taiwanese Journal of Mathematics
Volume	22
Issue number	6
DOIs	https://doi.org/10.11650/tjm/180204
Publication status	Published - 2018 Dec 1

Keywords

Maximal averages
Non-smooth and non-convex hypersurfaces

ASJC Scopus subject areas

Mathematics(all)

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title = "Maximal averages over certain non-smooth and non-convex hypersurfaces",

abstract = "We consider the maximal operators whose averages are taken over some non-smooth and non-convex hypersurfaces. For each 1 ≤ i ≤ d−1, let φi: [−1,1] → R be a continuous function satisfying some derivative conditions, and let (Formula presented). We prove the Lp boundedness of the maximal operators associated with the graph of φ which is a non-smooth and non-convex hypersurface in Rd, d ≥ 3.",

keywords = "Maximal averages, Non-smooth and non-convex hypersurfaces",

author = "Yaryong Heo and Sunggeum Hong and Yang, {Chan Woo}",

note = "Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology NRF-2015R1A1A1A05001304, NRF-2014R1A1A3049983, and NRF-2016R1D1A1B01014575.The authors would like to thank the referee for the careful reading and valuable suggestions to improve the presentation of this paper.",

year = "2018",

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doi = "10.11650/tjm/180204",

language = "English",

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T1 - Maximal averages over certain non-smooth and non-convex hypersurfaces

AU - Heo, Yaryong

AU - Hong, Sunggeum

AU - Yang, Chan Woo

N1 - Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology NRF-2015R1A1A1A05001304, NRF-2014R1A1A3049983, and NRF-2016R1D1A1B01014575.The authors would like to thank the referee for the careful reading and valuable suggestions to improve the presentation of this paper.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - We consider the maximal operators whose averages are taken over some non-smooth and non-convex hypersurfaces. For each 1 ≤ i ≤ d−1, let φi: [−1,1] → R be a continuous function satisfying some derivative conditions, and let (Formula presented). We prove the Lp boundedness of the maximal operators associated with the graph of φ which is a non-smooth and non-convex hypersurface in Rd, d ≥ 3.

AB - We consider the maximal operators whose averages are taken over some non-smooth and non-convex hypersurfaces. For each 1 ≤ i ≤ d−1, let φi: [−1,1] → R be a continuous function satisfying some derivative conditions, and let (Formula presented). We prove the Lp boundedness of the maximal operators associated with the graph of φ which is a non-smooth and non-convex hypersurface in Rd, d ≥ 3.

KW - Maximal averages

KW - Non-smooth and non-convex hypersurfaces

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