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
Let b ∈ L loc(? n ) and L denote the Littlewood-Paley operators including the Littlewood-Paley g function, Lusin area integral and g λ * function. In this paper, the authors prove that the L p boundedness of commuta...Let b ∈ L loc(? n ) and L denote the Littlewood-Paley operators including the Littlewood-Paley g function, Lusin area integral and g λ * function. In this paper, the authors prove that the L p boundedness of commutators [b, L] implies that b ∈ BMO(? n ). The authors therefore get a characterization of the L p -boundedness of the commutators [b, L]. Notice that the condition of kernel function of L is weaker than the Lipshitz condition and the Littlewood-Paley operators L is only sublinear, so the results obtained in the present paper are essential improvement and extension of Uchiyama’s famous result.展开更多
In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 （R^n） to L1 （R^n） and from ...In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 （R^n） to L1 （R^n） and from the weak Hardy space H^1,∞ （R^n） to L^1,∞ （R^n）, respectively. As corollaries of the above results, it is shown that μΩ,S^ρ is also an operator of weak type These conclusions are substantial improvement and （1, 1） and of type （p,p） for 1 〈 p 〈 2, respectively extension of 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.
基金supported by National Natural Science Foundation of China (Grant No. 10931001, 10826046)Specialized Research Foundation for Doctor Programme (Grant No. 20050027025)
文摘Let b ∈ L loc(? n ) and L denote the Littlewood-Paley operators including the Littlewood-Paley g function, Lusin area integral and g λ * function. In this paper, the authors prove that the L p boundedness of commutators [b, L] implies that b ∈ BMO(? n ). The authors therefore get a characterization of the L p -boundedness of the commutators [b, L]. Notice that the condition of kernel function of L is weaker than the Lipshitz condition and the Littlewood-Paley operators L is only sublinear, so the results obtained in the present paper are essential improvement and extension of Uchiyama’s famous result.
基金NSFC(Grant No.10571015)SRFDP of China(Grand No.20050027025)
文摘In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 （R^n） to L1 （R^n） and from the weak Hardy space H^1,∞ （R^n） to L^1,∞ （R^n）, respectively. As corollaries of the above results, it is shown that μΩ,S^ρ is also an operator of weak type These conclusions are substantial improvement and （1, 1） and of type （p,p） for 1 〈 p 〈 2, respectively extension of some known results.
