In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also...In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.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 give a new integral estimate of the Bessel function, which is an extension of Calderón-Zygmund’s result. As an application of this result, we prove that the parameterized Marcinkiewicz ...In this paper the authors give a new integral estimate of the Bessel function, which is an extension of Calderón-Zygmund’s result. As an application of this result, we prove that the parameterized Marcinkiewicz integral μ Ω ρ with variable kernels is of type (2, 2), where the kernel function Θ does not have any smoothness on the unit sphere in ? n .展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10571015)Specialized Research Foundation for Doctor Programme (Grant No. 20050027025)
文摘In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.
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the National Natural Science Foundation of China (Grant No.10571015) the Specialized Research Foundation for Doctor Programme (Grant No.20050027025)
文摘In this paper the authors give a new integral estimate of the Bessel function, which is an extension of Calderón-Zygmund’s result. As an application of this result, we prove that the parameterized Marcinkiewicz integral μ Ω ρ with variable kernels is of type (2, 2), where the kernel function Θ does not have any smoothness on the unit sphere in ? n .
