Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
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
Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz...Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.展开更多
Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. ...Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.展开更多
In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the bound...In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calder6n-Zygmund operators and multilinear Calderon-Zygmund operators with Dini type kernels.展开更多
Let 6=(bi,b2,...,bm)be a collection of locally integrable functions and T,the com-mutator of multilinear singular integral operator T.Denote by L(δ)and L(δ(·))the Lipschitz spaces and the variable Lipschitz spa...Let 6=(bi,b2,...,bm)be a collection of locally integrable functions and T,the com-mutator of multilinear singular integral operator T.Denote by L(δ)and L(δ(·))the Lipschitz spaces and the variable Lipschitz spaces,respectively.The main purpose of this paper is to establish some new characterizations of the(variable)Lipschitz spaces in terms of the boundedness of multilinear commutator T∑b in the context of the variable exponent Lebesgue spaces,that is,the authors give the necessary and sufficient conditions for bj(j=1,2,...,m)to be L(δ)or L(δ(·))via the boundedness of multilinear commutator from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces.The authors do so by applying the Fourier series technique and some pointwise esti-mate for the commutators.The key tool in obtaining such pointwise estimate is a certain generalization of the classical sharp maximal operator.展开更多
The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ) functions of Tolsa with non-doubling measures is obtained, provided that ∥μ∥ = ∞ and multilinear singular...The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ) functions of Tolsa with non-doubling measures is obtained, provided that ∥μ∥ = ∞ and multilinear singular integrals are bounded from L 1(μ) × L 1(μ) to L 1/2,∞(μ).展开更多
In this paper, we establish the boundedness of commutators generated by the multilinear Calderon- Zygmud type singular integrals and Lipschitz functions on the Triebel-Lizorkin space and Lipschitz spaces.
This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular in...This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar＇s inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.展开更多
This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO fu...This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.展开更多
In this paper, the boundedness of mulitilinear commutator [-b,T] on Herz-type space is considered, where T is a standard Calderon-Zygmund singular operator and -b ∈ （BMO（Rn））m.
In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our...In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.展开更多
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
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 the National Natural Science Foundation of China(10971228)Supported by the Science and Technology Innovation Plan for Graduate Students of Jiangsu Educational Department(CXZZll-0633)+1 种基金Supported by the Science and Technology Innovation Plan for Graduate Students of Nangtong University (YKC111051)Supported by the NSF of Nantong University(llZY002)
文摘Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.
文摘Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.
基金Supported by the National Natural Science Foundation of China(Grant No.11671397)the Fundamental Research Funds for the Central Universities(Grant No.2009QS16)+1 种基金the State Scholarship Fund of Chinathe Yue Qi Young Scholar of China University of Mining and Technology(Beijing)
文摘In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calder6n-Zygmund operators and multilinear Calderon-Zygmund operators with Dini type kernels.
基金Supported by the National Natural Science Foundation of China(Grant No.11571160)the Research Funds for the Educational Committee of Heilongjiang(Grant No.2019-KYYWF-0909)the Reform and Development Foundation for Local Colleges and Universities of the Central Government(Grant No.2020YQ07)。
文摘Let 6=(bi,b2,...,bm)be a collection of locally integrable functions and T,the com-mutator of multilinear singular integral operator T.Denote by L(δ)and L(δ(·))the Lipschitz spaces and the variable Lipschitz spaces,respectively.The main purpose of this paper is to establish some new characterizations of the(variable)Lipschitz spaces in terms of the boundedness of multilinear commutator T∑b in the context of the variable exponent Lebesgue spaces,that is,the authors give the necessary and sufficient conditions for bj(j=1,2,...,m)to be L(δ)or L(δ(·))via the boundedness of multilinear commutator from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces.The authors do so by applying the Fourier series technique and some pointwise esti-mate for the commutators.The key tool in obtaining such pointwise estimate is a certain generalization of the classical sharp maximal operator.
基金This work was partially supported by Scientific Research Fund of Hunan Provincial Education Department(Grant No.06B059)the Natural Science Foundation of Hunan Province of China(Grant No.06JJ5012)the National Natural Science Foundation of China(Grant Nos.60474070 and 10671062)
文摘The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ) functions of Tolsa with non-doubling measures is obtained, provided that ∥μ∥ = ∞ and multilinear singular integrals are bounded from L 1(μ) × L 1(μ) to L 1/2,∞(μ).
基金Supported by the National Natural Science Foundation of China(No.11161042,11271175)
文摘In this paper, we establish the boundedness of commutators generated by the multilinear Calderon- Zygmud type singular integrals and Lipschitz functions on the Triebel-Lizorkin space and Lipschitz spaces.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 10961015, 11261023, 10871024, 10931001, 11561057） and the Key Laboratory of Mathematics and Complex System, Ministry of Education, China.
文摘This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar＇s inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.
基金supported by the National Natural Science Foundation of China(Nos.10961015,11261023)the Jiangxi Natural Science Foundation of China(No.20122BAB201011)the Fund of Jiangxi Provincial Department of Education(Nos.GJJ10397,GJJ12203)
文摘This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.
基金Supported by the National Natural Science Foundation of China(10771054, 10861010)the Scientific Re-search Program of Institutions of Higher Education of XinJiang(2008S58)the Natural Science Fund of Xinjiang University(YX080106, BS090101)
文摘In this paper, the boundedness of mulitilinear commutator [-b,T] on Herz-type space is considered, where T is a standard Calderon-Zygmund singular operator and -b ∈ （BMO（Rn））m.
基金Supported by RFDP of China (Grant No. 20050027025)NSF of China (Grant No. 10571014, 10571015)
文摘In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.
