Abstract
In this paper, we study the L p boundedness for a class of maximal functions along surfaces in ℝn × ℝm of the form {(φ1(|u|)u′, φ2(|v|)v′) : (u,v) ∈ ℝn × ℝm}.We prove that such maximal functions are bounded on L p for all 2 ≤ p < ∞ provided that the functions φ1 and φ2 satisfy certain oscillatory estimates of van der Corput type.
| Original language | English |
|---|---|
| Pages (from-to) | 163-175 |
| Number of pages | 13 |
| Journal | Analysis Mathematica |
| Volume | 34 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sep 2008 |
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ASJC Scopus subject areas
- Mathematics(all)
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Maximal functions along surfaces on product domains. / Al-Salman, Ahmad.
In: Analysis Mathematica, Vol. 34, No. 3, 09.2008, p. 163-175.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Maximal functions along surfaces on product domains
AU - Al-Salman, Ahmad
PY - 2008/9
Y1 - 2008/9
N2 - In this paper, we study the L p boundedness for a class of maximal functions along surfaces in ℝn × ℝm of the form {(φ1(|u|)u′, φ2(|v|)v′) : (u,v) ∈ ℝn × ℝm}.We prove that such maximal functions are bounded on L p for all 2 ≤ p < ∞ provided that the functions φ1 and φ2 satisfy certain oscillatory estimates of van der Corput type.
AB - In this paper, we study the L p boundedness for a class of maximal functions along surfaces in ℝn × ℝm of the form {(φ1(|u|)u′, φ2(|v|)v′) : (u,v) ∈ ℝn × ℝm}.We prove that such maximal functions are bounded on L p for all 2 ≤ p < ∞ provided that the functions φ1 and φ2 satisfy certain oscillatory estimates of van der Corput type.
UR - http://www.scopus.com/inward/record.url?scp=51349107543&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=51349107543&partnerID=8YFLogxK
U2 - 10.1007/s10476-008-0301-8
DO - 10.1007/s10476-008-0301-8
M3 - Article
AN - SCOPUS:51349107543
VL - 34
SP - 163
EP - 175
JO - Analysis Mathematica
JF - Analysis Mathematica
SN - 0133-3852
IS - 3
ER -