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 ...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.展开更多
In this paper, boundedness and compactness of the composition operator on the generalized Lipschitz spaces Λα (α 〉 1) of holomorphic functions in the unit disk are characterized.
In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded...In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded from L^Pxy (R+) to L^qxδ (R+) with the bound explicitly worked out.展开更多
In this paper, the boundedness of commutators generated by the n- dimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are boun...In this paper, the boundedness of commutators generated by the n- dimensional 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 Hardy- Littlewood-Poly~ operator is also considered.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
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
In the present paper we extend previous results about the monotoaicity of Bernstein-type operators rdtiwe to convex functions and about the preservation of Lipschitz classes.
Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nons...Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...展开更多
In this note, the authors prove that the commutator Tb, generated by θ-type Calderon-Zygmund operator T and a Lipschitz function b is bounded from LP(R^n) intoLip(β_n/p)(R^n) and also maps from Ln/β (R^n) i...In this note, the authors prove that the commutator Tb, generated by θ-type Calderon-Zygmund operator T and a Lipschitz function b is bounded from LP(R^n) intoLip(β_n/p)(R^n) and also maps from Ln/β (R^n) into BMO(R^n).展开更多
In this paper, we discuss the boundedness of commutators of high dimensional Hausdorff operator He on Herz type spaces. In addition, central BMO estimates for such commutators are also presented.
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
Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process...Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process converges strongly to the unique solution of the equation Hx+Tx=f . This conclusion extends the corresponding results in recent papers.展开更多
In this paper,the King’s type modification of(p,q)-Bleimann-Butzer and Hahn operators is defined.Some results based on Korovkin’s approximation theorem for these new operators are studied.With the help of modulus of...In this paper,the King’s type modification of(p,q)-Bleimann-Butzer and Hahn operators is defined.Some results based on Korovkin’s approximation theorem for these new operators are studied.With the help of modulus of continuity and the Lipschitz type maximal functions,the rate of convergence for these new operators are obtained.It is shown that the King’s type modification have better rate of convergence,flexibility than classical(p,q)-BBH operators on some subintervals.Further,for comparisons of the operators,we presented some graphical examples and the error estimation in the form of tables through MATLAB(R2015a)展开更多
The boundedness of maximal Bochner-Riesz operator B^δ* and that of maximal commutator B^bδ*, generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space are establi...The boundedness of maximal Bochner-Riesz operator B^δ* and that of maximal commutator B^bδ*, generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space are established.展开更多
In this note, the authors show the boundedness of the maximal commutators of Bocher-Riesz operator B^δ and that of maximal commutator Bδ1^b, generated by B^δ and a Lipschitz function b mapping from Mp^q(R^n) into...In this note, the authors show the boundedness of the maximal commutators of Bocher-Riesz operator B^δ and that of maximal commutator Bδ1^b, generated by B^δ and a Lipschitz function b mapping from Mp^q(R^n) into BMO space and also maps from Mp^q(Rn) into L(βn/- q).展开更多
In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [<em>b</em>,<em>μ</em><sub>Ω</sub>] and obtain the result with ...In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [<em>b</em>,<em>μ</em><sub>Ω</sub>] and obtain the result with Lipschitz function and BMO function f on the Herz-Morrey-Hardy spaces with variable exponents <img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" width="0" height="0" alt="" /><img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" alt="" />.展开更多
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The NSF (Q2008A01) of Shandong,Chinathe NSF (10871024) of China
文摘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.
基金Supported in part by the National Natural Science Foundation of China (10971219)
文摘In this paper, boundedness and compactness of the composition operator on the generalized Lipschitz spaces Λα (α 〉 1) of holomorphic functions in the unit disk are characterized.
基金Supported in part by the Natural Science Foundation of China under the Grant 10771221Natural Science Foundation of Beijing under the Grant 1092004
文摘In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded from L^Pxy (R+) to L^qxδ (R+) with the bound explicitly worked out.
基金The NSF(11261055)of Chinathe NSF(2012211B28,2011211A005)of Xinjiangthe Open Foundation Project(2012ZDXK002)of Key Disciplines in Xinjiang
文摘In this paper, the boundedness of commutators generated by the n- dimensional 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 Hardy- Littlewood-Poly~ operator is also considered.
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.
文摘In the present paper we extend previous results about the monotoaicity of Bernstein-type operators rdtiwe to convex functions and about the preservation of Lipschitz classes.
基金Supported by the NNSF of China(10571014)SEDF of China(20040027001)
文摘Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...
基金Supported by NSFC(10571014)NSFC(10571156)+1 种基金the Doctor Foundation of Jxnu (2443)the Natural Science Foundation of Jiangxi province(2008GZS0051)
文摘In this note, the authors prove that the commutator Tb, generated by θ-type Calderon-Zygmund operator T and a Lipschitz function b is bounded from LP(R^n) intoLip(β_n/p)(R^n) and also maps from Ln/β (R^n) into BMO(R^n).
基金supported by NNSF of China(No.11271330)NNSF of Zhejiang(No.Y604563)PRSF ofZhejiang(No.BSH1302046)
文摘In this paper, we discuss the boundedness of commutators of high dimensional Hausdorff operator He on Herz type spaces. In addition, central BMO estimates for such commutators are also presented.
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.
文摘Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process converges strongly to the unique solution of the equation Hx+Tx=f . This conclusion extends the corresponding results in recent papers.
文摘In this paper,the King’s type modification of(p,q)-Bleimann-Butzer and Hahn operators is defined.Some results based on Korovkin’s approximation theorem for these new operators are studied.With the help of modulus of continuity and the Lipschitz type maximal functions,the rate of convergence for these new operators are obtained.It is shown that the King’s type modification have better rate of convergence,flexibility than classical(p,q)-BBH operators on some subintervals.Further,for comparisons of the operators,we presented some graphical examples and the error estimation in the form of tables through MATLAB(R2015a)
基金Supported by NSFC(10571014),NSFC(10571156)the growth foundation of JXNU (1983)the doctor founda-tion of JXNU.
文摘The boundedness of maximal Bochner-Riesz operator B^δ* and that of maximal commutator B^bδ*, generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space are established.
基金Supported by NNSF (10961015, 10871173)Supported by JXNSF (2008 Gzs0051,GJJ08169)
文摘In this note, the authors show the boundedness of the maximal commutators of Bocher-Riesz operator B^δ and that of maximal commutator Bδ1^b, generated by B^δ and a Lipschitz function b mapping from Mp^q(R^n) into BMO space and also maps from Mp^q(Rn) into L(βn/- q).
文摘In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [<em>b</em>,<em>μ</em><sub>Ω</sub>] and obtain the result with Lipschitz function and BMO function f on the Herz-Morrey-Hardy spaces with variable exponents <img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" width="0" height="0" alt="" /><img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" alt="" />.
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.