Characterization for commutators of n-dimensional fractional Hardy operators

In this paper, it was proved that the commutator Hβ,b generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from Lp1(Rn) to Lp2 (Rn) if and only if b is a C(M)O(Rn) function, where 1/p1 - 1/p2 = β/n, 1 ＜ p1 ＜∞, 0 ≤β＜ n. Furthemore,the characterization of Hβ,b on the homogenous Herz space (K)qα,p(Rn) was obtained.     

多线性分数次Hardy算子交换子的有界性

在齐次Morrey-Herz空间MK˙α,λp,q(Rn)上建立了由n维分数次Hardy算子和CBMO函数生成的多线性交换子H,b的有界性.     

Endpoint estimates for n-dimensional Hardy operators and their commutators

In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.     

Boundedness of higher order commutators of generalized fractional integral operators on Hardy spaces

Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.     

Lipschitz Estimates for Commutators of $N$-Dimensional Fractional Hardy Operators

In this paper, it is proved that the commutator$\mathcal{H}_{β,b}$ which is generated by the $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ and $b\in \dot{Λ}_α(\mathbb{R}^n)$ is bounded from $L^P(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$, where $0<α<1,1相似文献   

Lipschitz Estimates for Commutators of N-dimensional Fractional Hardy Operators

In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = （α＋β）/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p（R^n） is obtained.     

一类分数次算子在加权Herz型Hardy空间上的有界性

证明了一类分数次算子的ＨＫ_ｑ_１~（ａ,ｐ）（ｗ_１;ｗ_２~ｑ１）到Ｋ_ｑ_２~（ａ,ｐ）（ｗ_１;ｗ_２~ｑ２）和ＨＫ_ｑ_１~ａ_１~ｐ（１,ｘ~（βｑ_１）到Ｋ_ｑ_２~ａ_１~ｐ（１,ｘ~（βｑ_２）的有界性．     

Boundedness of commutators for Marcinkiewicz integrals on weighted Herz-type Hardy spaces

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.     

Bounds for commutators of multilinear fractional integral operators with homogeneous kernels

We will show bounds for commutators of multilinear fractional integral operators with some homogeneous kernels.     

Lipschitz Estimates for Commutators of p-adic Fractional Hardy Op erators

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.     

Boundedness of commutators of generalized fractional integral operators on weighted herz-type hardy spaces

In this paper, we study the boundedness of higher order commutators of generalized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.     

一类分数次积分算子在Herz型Hardy空间上的有界性

通过放宽尺寸条件,得到了一类具有分数次积分性质的次线性算子从Herz型Hardy空间到(弱)Herz型Hardy空间有界性的判定条件,以及端点处的弱型估计.     

CBMO estimates for multilinear Hardy operators

The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces.     

广义分数次积分算子在加权Herz型Hardy空间的有界性

利用加权Herz型Hardy空间的原子分解理论,讨论了广义分数次积分算子Tl从加权Lp空间到加权Lq空间,以及从加权Herz型Hardy空间到加权Herz空间的有界性问题.将已有的分数次积分算子的结论推广到广义分数次积分算子的情形.     

Boundedness of commutators on Hardy type spaces

Let [b, T] be the commutator of the function b ∈ Lipβ(Rn) (0 ＜β≤ 1) and the CalderónZygmund singular integral operator T. The authors study the boundedness properties of [b, T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme cases.     

Endpoint estimates for commutators of multilinear fractional integral operators

In this paper, the weak type LlogL estimate for the multilinear fractional commutator is obtained by introducing a new kind of maximal operator of the multilinear fractional order associated with the mean Luxumburg norm and using the technique of sharp function.     

多线性分数次积分算子交换子的有界性

Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1 01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(…     

Commutators of n-dimensional rough Hardy operators

In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.     

Boundedness for multilinear fractional integral operators on Herz type spaces

In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.     

Commutators of integral operators with variable kernels on Hardy spaces

LetT _Ω,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, T_Ω,α] be the commutator generated by T_Ω,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, T_Ω,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.