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.
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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 -