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

Ya-Ryong Heo; Sunggeum Hong; Chan Woo Yang

doi:10.11650/tjm/180204

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

Ya-Ryong Heo, Sunggeum Hong, Chan Woo Yang

Department of Mathematics

Research output: Contribution to journal › Article

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)

Access to Document

10.11650/tjm/180204

Fingerprint Dive into the research topics of 'Maximal averages over certain non-smooth and non-convex hypersurfaces'. Together they form a unique fingerprint.

Cite this

Heo, Y-R., Hong, S., & Yang, C. W. (2018). Maximal averages over certain non-smooth and non-convex hypersurfaces. Taiwanese Journal of Mathematics, 22(6), 1383-1401. https://doi.org/10.11650/tjm/180204

@article{21320b554fa643be9e9ee2ca3d0af603,

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 = "Ya-Ryong Heo and Sunggeum Hong and Yang, {Chan Woo}",

year = "2018",

month = dec,

day = "1",

doi = "10.11650/tjm/180204",

language = "English",

volume = "22",

pages = "1383--1401",

journal = "Taiwanese Journal of Mathematics",

issn = "1027-5487",

publisher = "Mathematical Society of the Rep. of China",

number = "6",

}

TY - JOUR

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

AU - Heo, Ya-Ryong

AU - Hong, Sunggeum

AU - Yang, Chan Woo

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

UR - http://www.scopus.com/inward/record.url?scp=85060085725&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060085725&partnerID=8YFLogxK

U2 - 10.11650/tjm/180204

DO - 10.11650/tjm/180204

M3 - Article

AN - SCOPUS:85060085725

VL - 22

SP - 1383

EP - 1401

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 6

ER -