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

Ya-Ryong Heo, Sunggeum Hong, Chan Woo Yang

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)1383-1401
Number of pages19
JournalTaiwanese Journal of Mathematics
Volume22
Issue number6
DOIs
Publication statusPublished - 2018 Dec 1

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Maximal Operator
Hypersurface
Boundedness
Continuous Function
Derivative
Graph in graph theory

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Maximal averages over certain non-smooth and non-convex hypersurfaces. / Heo, Ya-Ryong; Hong, Sunggeum; Yang, Chan Woo.

In: Taiwanese Journal of Mathematics, Vol. 22, No. 6, 01.12.2018, p. 1383-1401.

Research output: Contribution to journalArticle

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