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

Yaryong Heo, Sunggeum Hong, Chan Woo Yang

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1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)1383-1401
Number of pages19
JournalTaiwanese Journal of Mathematics
Issue number6
Publication statusPublished - 2018 Dec 1

Bibliographical 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.

Publisher Copyright:
© 2018, Mathematical Society of the Rep. of China. All rights reserved.


  • Maximal averages
  • Non-smooth and non-convex hypersurfaces

ASJC Scopus subject areas

  • General Mathematics


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