Let α∈（0,∞ ）, p, q ∈[1, ∞）, s be a nonnegative integer, and ω∈ A1（Rn） （tne class of Muckenhoupt＇s weights）. In this paper, we introduce the generalized weighted Morrey- Campanato space L（α, p, q, s, ...Let α∈（0,∞ ）, p, q ∈[1, ∞）, s be a nonnegative integer, and ω∈ A1（Rn） （tne class of Muckenhoupt＇s weights）. In this paper, we introduce the generalized weighted Morrey- Campanato space L（α, p, q, s, ω; Rn） and obtain its equivalence on different p∈ [1, β） and 1 integers s ≥[nα] （the integer part of nα）, whereβ = （1/q - α）-1 when α 〈 1/qorβ= ∞ when α ≥1/q We then introduce the generalized weighted Lipschitz space A（α, q, w; Rn） and prove that L（a, p, q, s, w; Rn）С ∧（α, q, w; Rn） when α ∈ （0, ∞）, s ≥[nα], and p∈ [1,β）.展开更多
In this paper, we define β-Hausdorff operator on the unit polydisk and study the boundedness of the operator on Lipschitz space. Firstly, we translate the problem of coefficient into integral of weighted composition ...In this paper, we define β-Hausdorff operator on the unit polydisk and study the boundedness of the operator on Lipschitz space. Firstly, we translate the problem of coefficient into integral of weighted composition operator, then give the sufficient conditions of boundedness, and also obtain an upper bound for the operator norm on Lipschitz space.展开更多
Littlewood-Paley operators, the g-function, the area integral and the function g^＊λ, are considered as operators on weighted Lipschitz spaces. It is proved that the image of a weighted Lipschitz function under one o...Littlewood-Paley operators, the g-function, the area integral and the function g^＊λ, are considered as operators on weighted Lipschitz spaces. It is proved that the image of a weighted Lipschitz function under one of these operators is either equal to infinity almost everywhere or is in weighted Lipschitz spaces.展开更多
In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appro...In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appropriate conditions on the weight w, where b belongs to Lipschitz space or weighted Lipschitz space.展开更多
Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this pa...Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.展开更多
In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on Lipschitz domains. Also, we give their application for the harmonic function defined in bounded Lipschitz domains.
In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip;（R;）,（0 <β≤1） and T is aθ（t）-type Calderón-Zygmund operator. The commutator [b,T] gener...[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip;（R;）,（0 <β≤1） and T is aθ（t）-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f（x）=b（x）Tf（x）-T（bf）(x)=∫k（x,y）(b（x）-b（y）)f（y）dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H;（ω;） to L;（ω;）, and from HK;(ω;,ω;) to K;(ω;,ω;). The results extend and generalize the well-known ones in [7].展开更多
基金supported by the National Natural Science Foundation of China(10871025)
文摘Let α∈（0,∞ ）, p, q ∈[1, ∞）, s be a nonnegative integer, and ω∈ A1（Rn） （tne class of Muckenhoupt＇s weights）. In this paper, we introduce the generalized weighted Morrey- Campanato space L（α, p, q, s, ω; Rn） and obtain its equivalence on different p∈ [1, β） and 1 integers s ≥[nα] （the integer part of nα）, whereβ = （1/q - α）-1 when α 〈 1/qorβ= ∞ when α ≥1/q We then introduce the generalized weighted Lipschitz space A（α, q, w; Rn） and prove that L（a, p, q, s, w; Rn）С ∧（α, q, w; Rn） when α ∈ （0, ∞）, s ≥[nα], and p∈ [1,β）.
文摘In this paper, we define β-Hausdorff operator on the unit polydisk and study the boundedness of the operator on Lipschitz space. Firstly, we translate the problem of coefficient into integral of weighted composition operator, then give the sufficient conditions of boundedness, and also obtain an upper bound for the operator norm on Lipschitz space.
基金The Scienctific Research Fund of Chongqing Municipal Education Commission (021201)
文摘Littlewood-Paley operators, the g-function, the area integral and the function g^＊λ, are considered as operators on weighted Lipschitz spaces. It is proved that the image of a weighted Lipschitz function under one of these operators is either equal to infinity almost everywhere or is in weighted Lipschitz spaces.
基金supported by NSFC (NO. 11201003)Education Committee of Anhui Province (NO. KJ2011A138 and NO. KJ2012A133)
文摘In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appropriate conditions on the weight w, where b belongs to Lipschitz space or weighted Lipschitz space.
文摘Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.
基金Project supported by the National Natural Science Foundation of China (No. 10377108)the Natural Science Foundation of Guangdong Province (No. 031495), China
文摘In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on Lipschitz domains. Also, we give their application for the harmonic function defined in bounded Lipschitz domains.
文摘In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
文摘[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip;（R;）,（0 <β≤1） and T is aθ（t）-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f（x）=b（x）Tf（x）-T（bf）(x)=∫k（x,y）(b（x）-b（y）)f（y）dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H;（ω;） to L;（ω;）, and from HK;(ω;,ω;) to K;(ω;,ω;). The results extend and generalize the well-known ones in [7].
