We give the L<sup>p</sup>-boundedness for a class of Marcinkiewicz integral operators μΩ, μ<sub>Ω.λ</sub> and μ<sub>Ω.S</sub> related to the Littlewood-Paley g-function, g<...We give the L<sup>p</sup>-boundedness for a class of Marcinkiewicz integral operators μΩ, μ<sub>Ω.λ</sub> and μ<sub>Ω.S</sub> related to the Littlewood-Paley g-function, g<sub>λ</sub><sup>-</sup>function and the area integral S, respectively. These operators have the kernel functions Ω∈H<sup>1</sup>(S<sup>n-1</sup>), the Hardy space on S<sup>n-1</sup>. The results in this paper substantially improve and extend the known results.展开更多
In this paper the authors give the weighted weak LlogL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities...In this paper the authors give the weighted weak LlogL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities for the Marcinkiewicz integral and its commutators with different weight functions are also discussed.展开更多
Let(X,d,μ)be a metric measure space satisfying the upper doubling condition and the geometrically doubling condition in the sense of Hyto¨nen.We prove that the L p(μ)-boundedness with p∈(1,∞)of the Marcinkiew...Let(X,d,μ)be a metric measure space satisfying the upper doubling condition and the geometrically doubling condition in the sense of Hyto¨nen.We prove that the L p(μ)-boundedness with p∈(1,∞)of the Marcinkiewicz integral is equivalent to either of its boundedness from L1(μ)into L1,∞(μ)or from the atomic Hardy space H1(μ)into L1(μ).Moreover,we show that,if the Marcinkiewicz integral is bounded from H1(μ)into L1(μ),then it is also bounded from L∞(μ)into the space RBLO(μ)(the regularized BLO),which is a proper subset of RBMO(μ)(the regularized BMO)and,conversely,if the Marcinkiewicz integral is bounded from L∞b(μ)(the set of all L∞(μ)functions with bounded support)into the space RBMO(μ),then it is also bounded from the finite atomic Hardy space H1,∞fin(μ)into L1(μ).These results essentially improve the known results even for non-doubling measures.展开更多
In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ（R^n）（0 〈β≤ 1/m） and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on t...In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ（R^n）（0 〈β≤ 1/m） and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on the Hardy type spaces Hb^m^p,n（R^n） and the Herz Hardy type spaces Hbm Kq^α,p（R^b）.展开更多
In the present paper, we consider the boundedness of Marcinkiewicz integral operator μΩ,h,Ф along a surface Г = {x = Ф（｜y｜）y/｜y｜）} on the Triebel-Lizorkin space Fq,q^α（R^n ） for Ω belonging to H1 （Sn-...In the present paper, we consider the boundedness of Marcinkiewicz integral operator μΩ,h,Ф along a surface Г = {x = Ф（｜y｜）y/｜y｜）} on the Triebel-Lizorkin space Fq,q^α（R^n ） for Ω belonging to H1 （Sn-1） and some class WFα（S^n-1）, which relates to Grafakos-Stefanov class. Some previous results are extended and improved.展开更多
In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.
The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn × Rm) to the Lebesgue space L1(Rn × Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn &...The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn × Rm) to the Lebesgue space L1(Rn × Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn × Rm) to the Lebesgue space Lq(Rn × Rm) for some q＞1.展开更多
In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions ...In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.展开更多
基金The first anthor is supported by NSF of China (Grant No. 19971010) DPFIIIF of China and the third anthor is supported in part by NSF Grant DMS 9622979
文摘We give the L<sup>p</sup>-boundedness for a class of Marcinkiewicz integral operators μΩ, μ<sub>Ω.λ</sub> and μ<sub>Ω.S</sub> related to the Littlewood-Paley g-function, g<sub>λ</sub><sup>-</sup>function and the area integral S, respectively. These operators have the kernel functions Ω∈H<sup>1</sup>(S<sup>n-1</sup>), the Hardy space on S<sup>n-1</sup>. The results in this paper substantially improve and extend the known results.
文摘In this paper the authors give the weighted weak LlogL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities for the Marcinkiewicz integral and its commutators with different weight functions are also discussed.
基金supported by the Mathematical Tianyuan Youth Fund of the National Natural Science Foundation of China (Grant No. 11026120)Chinese Universities Scientific Fund (Grant No. 2011JS043)+1 种基金National Natural Science Foundation of China (Grant Nos. 11171027 and 11361020)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120003110003)
文摘Let(X,d,μ)be a metric measure space satisfying the upper doubling condition and the geometrically doubling condition in the sense of Hyto¨nen.We prove that the L p(μ)-boundedness with p∈(1,∞)of the Marcinkiewicz integral is equivalent to either of its boundedness from L1(μ)into L1,∞(μ)or from the atomic Hardy space H1(μ)into L1(μ).Moreover,we show that,if the Marcinkiewicz integral is bounded from H1(μ)into L1(μ),then it is also bounded from L∞(μ)into the space RBLO(μ)(the regularized BLO),which is a proper subset of RBMO(μ)(the regularized BMO)and,conversely,if the Marcinkiewicz integral is bounded from L∞b(μ)(the set of all L∞(μ)functions with bounded support)into the space RBMO(μ),then it is also bounded from the finite atomic Hardy space H1,∞fin(μ)into L1(μ).These results essentially improve the known results even for non-doubling measures.
文摘In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ（R^n）（0 〈β≤ 1/m） and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on the Hardy type spaces Hb^m^p,n（R^n） and the Herz Hardy type spaces Hbm Kq^α,p（R^b）.
基金partially supported by Grant-in-Aid for Scientific Research(C)(No.23540228),Japan Society for the Promotion of Science
文摘In the present paper, we consider the boundedness of Marcinkiewicz integral operator μΩ,h,Ф along a surface Г = {x = Ф（｜y｜）y/｜y｜）} on the Triebel-Lizorkin space Fq,q^α（R^n ） for Ω belonging to H1 （Sn-1） and some class WFα（S^n-1）, which relates to Grafakos-Stefanov class. Some previous results are extended and improved.
基金Supported by the National Science Foundation of China (Grants 10901043, 10701064, 10871173, and 10931001)Hangdian Foundation (KYS075608076)
文摘In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.
基金This work was supported by the National Science Foundation for Distinguished Young Scholars(Grant No.10425106)Program for New Century Excellent Talents in University(Grant No.04-0142)of Ministry of Education of China.
文摘The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn × Rm) to the Lebesgue space L1(Rn × Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn × Rm) to the Lebesgue space Lq(Rn × Rm) for some q＞1.
基金Supported by the NSF of China (G10571122) the NFS of Fujian Province of China (Z0511004)
文摘In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.
