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1.
Let[b,T]be the commutator generated by a Lipschitz function b ∈ Lip(β)(0<β<1)and multiplierT.The authors studied the boundedness of[b,T]on the Lebesgue spaces and Hardy spaces.  相似文献   

2.
In this paper, two classes of closely related multilinear singular and fractional integrals,which include the commutators as special cases, are studied and their boundedness on Herz type spaces is discussed. In fact, it is proved that these operators are actually not bounded in certain extreme cases.  相似文献   

3.
In this paper, the boundedness of commutators generated by the ndimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are bounded on Herz space and Lebesgue space with suitable indexes. Moreover, the commutator of HardyLittlewood-Poly′a operator is also considered.  相似文献   

4.
Shanzhen  Lu  Lifang  Xu 《分析论及其应用》2004,20(3):215-230
In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 <α≤ 1).  相似文献   

5.
In this paper, the authors introduce a class of product anisotropic singular integral operators, whose kernels are adapted to the action of a pair A := (A1, A2) of expansive dilations on R n and R m , respectively. This class is a generalization of product singular integrals with convolution kernels introduced in the isotropic setting by Fefferman and Stein. The authors establish the boundedness of these operators in weighted Lebesgue and Hardy spaces with weights in product A∞ Muckenhoupt weights on R n × R m . These results are new even in the unweighted setting for product anisotropic Hardy spaces.  相似文献   

6.
Let[b,T]be the commutator of parabolic singular integral T.In this paper,the authors prove that the boundedness of[b,T]on the generalized Morrey spaces implies b∈BM O(Rn,ρ).The results in this paper improve and extend the Komori and Mizuhara’s results.  相似文献   

7.
In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ(R^n)(0 〈β≤ 1/m) and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on the Hardy type spaces Hb^m^p,n(R^n) and the Herz Hardy type spaces Hbm Kq^α,p(R^b).  相似文献   

8.
In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral μΩ^b, multilinear Marcinkiewicz integral μΩ^A and its variation μΩ^A on Herz-type Hardy spaces, here Ω is homogeneous of degree zero and satisfies a class of L^s-Dini condition. And as a special case, they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-type Hardy spaces.  相似文献   

9.
Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b,Iα] is continuous from an atomic Hardy space Hp b into Lp, where Hp b is a subspace of the Hardy space Hp for n/(n + 1) 〈 p ≤ 1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint (Hp1 b1 ×... × HP2, Lp) boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderdn-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b ∈ (Lipβ)m(Rn).  相似文献   

10.
Let b ∈ Lloc(Rn) and L denote the Littlewood-Paley operators including the LittlewoodPaley g function,Lusin area integral and gλ* function. In this paper,the authors prove that the Lp boundedness of commutators [b,L] implies that b ∈ BMO(Rn) . The authors therefore get a characterization of the Lp-boundedness of the commutators [b,L]. Notice that the condition of kernel function of L is weaker than the Lipshitz condition and the Littlewood-Paley operators L is only sublinear,so the results obtained in the p...  相似文献   

11.
In this paper,the authors study the boundedness of the operator μ b Ω,the commutator generated by a function b ∈Lip β (R n)(0 < β < 1) and the Marcinkiewicz integral μΩ on weighted Herz-type Hardy spaces.  相似文献   

12.
LetT Ω,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, TΩ,α] be the commutator generated by TΩ,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, TΩ,α] on the Hardy spaces, under some assumptions such as theL r -Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators . The smoothness conditions imposed on are weaker than the corresponding known results.  相似文献   

13.
In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained.  相似文献   

14.
LetHa,b be the commutator generated by the generalized Hardy operator and the CMO function. The (Lp, Lp) boundedness of Ha,b is discussed in this paper. Furthermore, the authors consider the boundedness of Ha,b on the weighted homogeneous Herz spaces (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

15.
Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition, the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calderon-Zygmund operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H1 (μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measureμis the d-dimensional Lebesgue measure.  相似文献   

16.
陶祥兴  张松艳 《数学学报》2011,54(1):97-110
设Ω是球面上函数,b是径向函数,ρ是实部正的复数;设Ψ为C~2([0,∞))的递增凸函数,Ψ(0)=0.本文研究非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,b)~ρ,以及旋转曲面上的非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,Ψ,b)~ρ,给出非齐次粗糙核Ω和b的最小光滑性条件,建立算子μ_(Ω,b)~ρ和μ_(Ω,Ψ,b)~ρ在Hardy空间和弱Hardy空间上的有界性.本文结果推进了先前b≡1情形的已有工作.  相似文献   

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