数学学报
數學學報
수학학보
ACTA MATHEMATICA SINCA
2001年
3期
527-534
,共8页
Marcinkiewicz积分%Littlewood-Paley g-函数和g*λ函数%面积积分%H1(Sn-1)空间%粗糙核
Marcinkiewicz積分%Littlewood-Paley g-函數和g*λ函數%麵積積分%H1(Sn-1)空間%粗糙覈
Marcinkiewicz적분%Littlewood-Paley g-함수화g*λ함수%면적적분%H1(Sn-1)공간%조조핵
本文证明了一类分别相应于Littlewood-Paley g函数,g*λ函数和面积积分S的Marcinkiewicz积分算子μΩ,μ*Ω,λ和μΩ,S的Lp(Rn)有界性.其中核函数Ω∈H1(Sn-1),这里H1(Sn-1)记Rn(n≥2)中的单位球面Sn-1上的Hardy空间.本文结果是已知结果的本质改进和推广.
本文證明瞭一類分彆相應于Littlewood-Paley g函數,g*λ函數和麵積積分S的Marcinkiewicz積分算子μΩ,μ*Ω,λ和μΩ,S的Lp(Rn)有界性.其中覈函數Ω∈H1(Sn-1),這裏H1(Sn-1)記Rn(n≥2)中的單位毬麵Sn-1上的Hardy空間.本文結果是已知結果的本質改進和推廣.
본문증명료일류분별상응우Littlewood-Paley g함수,g*λ함수화면적적분S적Marcinkiewicz적분산자μΩ,μ*Ω,λ화μΩ,S적Lp(Rn)유계성.기중핵함수Ω∈H1(Sn-1),저리H1(Sn-1)기Rn(n≥2)중적단위구면Sn-1상적Hardy공간.본문결과시이지결과적본질개진화추엄.
We give the LP-boundedness for a class of Marcinkiewicz integral operatorsμΩ, μ*Ω,λ and μΩ,s related to the Littlewood-Paley g-function, g~-function and thearea integral S, respectively. These operators have the kernel functions Ω ∈ H1(Sn-1),the Hardy space on Sn-1. The results in this paper substantially improve and extendthe known results.