数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2003年
6期
677-682
,共6页
奇异积分%粗糙核%曲面%极大算子
奇異積分%粗糙覈%麯麵%極大算子
기이적분%조조핵%곡면%겁대산자
singular integral%rough kernel%surface of revolution%maximal operator
本文建立了具有粗糙核的沿曲面奇异积分算子的Lp有界性.其中粗糙核K(y)=Ω(y)/|y|n,y∈Rn以及曲面{(y,φ(|y|)):y∈Rn}满足某种光滑条件.同时,相应极大算子的有界性也被得到.
本文建立瞭具有粗糙覈的沿麯麵奇異積分算子的Lp有界性.其中粗糙覈K(y)=Ω(y)/|y|n,y∈Rn以及麯麵{(y,φ(|y|)):y∈Rn}滿足某種光滑條件.同時,相應極大算子的有界性也被得到.
본문건립료구유조조핵적연곡면기이적분산자적Lp유계성.기중조조핵K(y)=Ω(y)/|y|n,y∈Rn이급곡면{(y,φ(|y|)):y∈Rn}만족모충광활조건.동시,상응겁대산자적유계성야피득도.
Let n ≥ 2. In this paper, the authors establish the Lp(Rn )-boundedness of a class of singular integral operators associated to surfaces of revolution, {(t, φ(|t|)) : t ∈ Rn }, with rough kernels for some p, if φ satisfies some smooth conditions.
