This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.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
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
[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
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.
Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,...Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,where the range of p is different from(1,∞),and we isolate the right class of weights introduced by Auscher and Martell.In this work,we use good-λ inequality with two parameters through the weighted boundedness of Riesz transforms ▽L^(-1/2).Our result recovers,in some sense,a previous result of Hofmann.展开更多
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
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[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].
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.
基金supported by NSFC(1187109611471033)+4 种基金supported by NSFC(113710571147103311571160)SRFDP(20130003110003)the Fundamental Research Funds for the Central Universities(2014KJJCA10)。
文摘Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,where the range of p is different from(1,∞),and we isolate the right class of weights introduced by Auscher and Martell.In this work,we use good-λ inequality with two parameters through the weighted boundedness of Riesz transforms ▽L^(-1/2).Our result recovers,in some sense,a previous result of Hofmann.