Mixed radial-angular integrability for rough maximal singular integrals and Marcinkiewicz integrals with mixed homogeneity

This paper is devoted to studying maximal singular integrals and Marcinkiewicz integrals with rough kernels in a mixed homogeneity setting. Assuming that the kernels satisfy certain rather weak size conditions, the boundedness of such operators on the mixed radial-angular spaces are established, respectively. Meanwhile, the corresponding vector-valued versions are also given.     

Generalized commutators for Marcinkiewicz type integrals with variable kernels

Let A be a function with derivatives of order m and D γ A ∈■β (0 < β < 1, |γ| = m). The authors in the paper prove that if Ω(x, z) ∈ L ∞ (R n ) × L s (S n 1 ) (s ≥ n/(n β)) is homogenous of degree zero and satisfies the mean value zero condition about the variable z, then both the generalized commutator for Marcinkiewicz type integral μ A Ω and its variation μ A Ω are bounded from L p (R n ) to L q (R n ), where 1 < p < n/β and 1/q = 1/p β/n. The authors also consider the boundedness of μ A Ω and its variation μ A Ω on Hardy spaces.     

关于分数次Marcinkiewicz积分在Hardy空间上的有界性

本文研究了核函数粗糙的分数次Marcinkiewicz积分μΩ,α在Hardy空间上的有界性.利用Hardy空间的原子分解定理,获得了算子μΩ,α的H1,Ln-nα型和(Hp,Lq)型的有界性结果.     

Weighted endpoint estimates for commutators of Marcinkiewicz integrals

Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO（R^n）. The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of Dini conditions, which improves the known result essentially.     

Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces

We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case.     

Marcinkiewicz积分交换子的弱型(H1,L1)估计

§1Introductionandstatementofresult DenotebySn-1theunitsphereinRn(n≥2)equippedwiththenormalizedLebesgue measuredx′=dσ(x′).LetΩ∈L1(Sn-1)behomogeneousofdegreezeroandsatisfy∫Sn-1Ω(x′)dx′=0.(1.1)Then-dimensionalMarcinkiewiczintegralcorrespondingtotheLittlewood-Paleyg-functionintroducedbyStein[1]isdefinedbyμΩ(f)(x)=∫∞0|FΩ,t(f)(x)|2dtt31/2,where FΩ,t(f)(x)=∫|x-y|≤tΩ(x-y)|x-y|n-1f(y)dy.In1958,Stein[1]provedthatifΩ∈Lipγ(Sn-1)(0<γ≤1),thenμΩisoftype(p,p)for1相似文献   

参数型Marcinkiewicz积分交换子在Hardy空间的有界性(英文)

研究了参数型Marcinkiewicz积分高阶交换子并证明了其从H1b(Rn)到L1(Rn)有界,其中b∈BMO.     

Marcinkiewicz积分在Herz型Hardy空间上的性质

给出了Marcinkiewicz积分在Herz型Hardy空间上的有界性证明。即当n(1 - 1q) ≤α 相似文献