| 粗糙平方函数及极大算子的弱型估计 |
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| 引用本文： | 姚奎.粗糙平方函数及极大算子的弱型估计[J].高校应用数学学报(英文版),2001,16(2):161-170. |
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| 作者姓名： | 姚奎 |
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| 作者单位： | 姚奎,Ying Yiming(Dept. of Math., Zhejiang Univ.(XiXi Campus));Yao Kui,Yao Kui(Institute of Sciences,PLA Univ. of Science and Technology,)
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| 基金项目： | Supported by NNSFC and NSFZJ |
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| 摘 要： | § 1 PreliminariesWe considerψ( x)∈ L1 ( Rn) satisfying the mean valuezero,i.e.∫Rnψdx=0 ,and definethe square function g( f) on Rnbyg( f) ( x) =( k|ψk* f|2 ) 1 2 ( x)for f∈ S( Rn) ,the Schwartz space,whereψk( x) =ψ2 k( x) . Whenψ has some smooth property,one can obtain the weak type estimate by viewingthe square function g( f) as the vector-valued singularintegrals,which the readercan referto 1 ,2 ] .As for the results aboutthe Lp-estimates,see 3,4 ] .In this paper,we sha…
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| 关 键 词： | 粗糙平方函数 极大算子 弱型估计 有界性 |
| 收稿时间： | 15 November 1999 |
Weak bounds for rough square and maximal operators |
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| Ying Yiming,Yao Kui.Weak bounds for rough square and maximal operators[J].Applied Mathematics A Journal of Chinese Universities,2001,16(2):161-170. |
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| Authors: | Ying Yiming Yao Kui |
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| Abstract: | With ΩεL (log+
L)(S
n−1
) and suitable h ∈ L
γ
(R
I)(1<γ⩽2), the weak type (1, 1) of the square function
and the maximal operator
were
, are studied in this paper. As a corollary, the weak bounds of M
Ω
(f)proved by Christ in 1988 are given and the previous weak type results for M
ϕ
(f)(x)are improved. In addition, the weighted weak type (1,1) estimates of the Littlewood-Paley function g
ϕ
(f) with power weights is also proved.
Supported by NNSFC and NSFZJ |
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| Keywords: | Square functions maximal operators rough kernel power weight |
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