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 language | English |
|---|---|
| Pages (from-to) | 1383-1401 |
| Number of pages | 19 |
| Journal | Taiwanese Journal of Mathematics |
| Volume | 22 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2018 Dec 1 |
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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 journal › Article
}
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 -