Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf...Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1.展开更多
In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to CalderSn-Zygmund singular integral operators, oscillatory singu...In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to CalderSn-Zygmund singular integral operators, oscillatory singular integral operators and parabolic difference equations are considered.展开更多
Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO（R^n）. The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of D...Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO（R^n）. The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of Dini conditions, which improves the known result essentially.展开更多
The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral opera...The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.展开更多
In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2...In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2（｜x｜^t; ｜x｜^t） and HK^α,P 2（｜x｜^t; ｜x｜^t）.展开更多
讨论了如下定义的带粗糙核的超奇异积分算子:TΩ,α,hf(x)=p.v.∫Rnh(|y|)(Ω(y′))/(|y|(n+a))f(x-y)dy的(Lαp(ω),Lαp(ω))有界性,推广了已有的结果.这里0≤α<1,1<p<∞,Ω为Hq(Sn-1)中的函数,q=(n-1)/(n-1+α),且h(|y|)...讨论了如下定义的带粗糙核的超奇异积分算子:TΩ,α,hf(x)=p.v.∫Rnh(|y|)(Ω(y′))/(|y|(n+a))f(x-y)dy的(Lαp(ω),Lαp(ω))有界性,推广了已有的结果.这里0≤α<1,1<p<∞,Ω为Hq(Sn-1)中的函数,q=(n-1)/(n-1+α),且h(|y|)∈△γ(R+)={sup R-1 integral (|h(t)|γdt) from n=0 to R},γ>1,R>0,ω是某类径向权.展开更多
In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the w...In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.展开更多
In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈...In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.展开更多
基金Hei Long Jiang Postdoctoral Foundation (LBH-Q06002)
文摘Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1.
基金Supported by National Natural Science Foundation of China(Grant Nos.10901076and11271175)National Natural Science Foundation of Shandong Province(Grant No.ZR2012AQ026)the Key Laboratory of Mathematics and Complex System (Beijing Normal University),Ministry of Education,China
文摘In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to CalderSn-Zygmund singular integral operators, oscillatory singular integral operators and parabolic difference equations are considered.
基金Supported by Postdoctoral Foundation of Hei Long Jiang Province (Grant No. LBH-Q06002)
文摘Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO（R^n）. The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of Dini conditions, which improves the known result essentially.
基金Project supported by the National Natural Science Foundation of China (No. 10771110)the Major Project of the Ministry of Education of China (No. 309018)
文摘The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.
基金Research is supported in part by National Science Council in Taipei
文摘In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2（｜x｜^t; ｜x｜^t） and HK^α,P 2（｜x｜^t; ｜x｜^t）.
文摘讨论了如下定义的带粗糙核的超奇异积分算子:TΩ,α,hf(x)=p.v.∫Rnh(|y|)(Ω(y′))/(|y|(n+a))f(x-y)dy的(Lαp(ω),Lαp(ω))有界性,推广了已有的结果.这里0≤α<1,1<p<∞,Ω为Hq(Sn-1)中的函数,q=(n-1)/(n-1+α),且h(|y|)∈△γ(R+)={sup R-1 integral (|h(t)|γdt) from n=0 to R},γ>1,R>0,ω是某类径向权.
基金supported in part by National Natural Foundation of China (Grant No. 11161042 and No. 11071250)
文摘In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.
文摘In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.
