Lp Estimates of certain rough parametric Marcinkiewicz functions

We prove L^p estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^{\mathrm{1}}(S^{n-\mathrm{1}}) integrability condition. The obtained L^p estimates resolve a problem left open in previous work. Our argument is based on duality technique and direct estimation of operators. As a consequence of our result, we deduce the L^p boundedness of a class of fractional Marcinkiewicz integral operators.     

Rough Marcinkiewicz integrals with mixed homogeneity on product spaces

In this paper, the parabolic Marcinkiewicz integral operators on the product spaces Rm × Rn (m, n≥ 2) are studied. The Lp -boundedness for such operators are established under rather weak size conditions of the kernels, which essentially improve or extend certain previous results.     

Parabolic Marcinkiewicz integrals along surfaces on product domains

In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain ℝ ⁿ × ℝ ^m (n,m ⩾ 2) are introduced. L ^p bounds of such operators are obtained under weak conditions on the kernels.     

On Marcinkiewicz integrals associated to compound mappings with rough kernels

The Lp bounds for the parametric Marcinkiewicz integrals associated to compound mapq pings, which contain many classical surfaces as model examples, are given, where the kernels of our operators are rather rough on the unit sphere as well as in the radial direction. These results substan- tially improve and extend some known results.     

沿复合子簇的粗糙核极大算子

给出了两类相关于沿复合子簇的粗糙核奇异积分的极大算子的L~p有界性,本质上极大地改进和一般化了已有的结果.作为应用,相关的奇异积分,Marcinkiewicz积分和相应的极大算子的L~p有界性也被建立.     

Rough Marcinkiewicz integrals along certain smooth curves

This paper is devoted to the study of the multiple-parameter rough Marcinkiewicz integral operators associated with certain smooth curves. It is shown that the Grafakos-Stefanov type size condition F_α (S^m-1 × S^n-1) of the kernel implies the L^p-boundedness of these Marcinkiewicz integral operators for some α>1/2 and 1+12α<p<1+2α, which is an essential improvement of certain previous results.     

广义Campanato空间上粗糙核参数型Marcinkiewicz积分

作为一类Littlewood-Paley函数,μ_(Ω,b)~ρ(f)是带非齐次粗糙核的参数型Marcinkiewicz积分,其中粗糙核Ω∈L~q(S~(n-1))满足消失性和积分Dini连续,径向核b∈Δ_s(R~+)∩Θ_s(R~n),1q,s∞,复参数ρ具有正实部.仅在一点有限的假设下,该文建立了μ_(Ω,b)~ρ(f)在广义Campanato空间L~(p,φ)(R~n)上的存在性和有界性,本质地推进了众多的已有工作.     

A Note on a Marcinkiewicz Integral Operator

We prove the L_p boundedness of Marcinkiewicz integral operators with rough kernels on ℝⁿ and T ⁿ.     

粗糙核带参数的抛物型Marcinkiewicz函数的一个注记

主要研究了带参数的抛物型Marcinkiewicz函数μσΩ,h（f）的L2（（R）n）有界性,用核的分解技术和Fourier变换估计的方法分别在当1＜-γ＜∞,h∈Hγ＇（IR）＋）,Ω∈L（logL）1/γ（Sn-1）条件下和当1〈γ≤∞,h∈△γ（（IR）＋）,Ω∈Llog＋L（Sn-1）条件下,建立了μσΩ,h（f）的L2（（R）n）有界性,并推广了以前学者的结论.     

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.     

A note on Marcinkiewicz integral operators

This paper is primarily concerned with proving the L^p boundedness of Marcinkiewicz integral operators with kernels belonging to certain block spaces. We also show the optimality of our condition on the kernel for the L² boundedness of the Marcinkiewicz integral.     

非齐次粗糙核参数型Marcinkiewicz算子的H~p有界性

设Ω是球面上函数,b是径向函数,ρ是实部正的复数;设Ψ为C~2([0,∞))的递增凸函数,Ψ(0)=0.本文研究非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,b)~ρ,以及旋转曲面上的非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,Ψ,b)~ρ,给出非齐次粗糙核Ω和b的最小光滑性条件,建立算子μ_(Ω,b)~ρ和μ_(Ω,Ψ,b)~ρ在Hardy空间和弱Hardy空间上的有界性.本文结果推进了先前b≡1情形的已有工作.     

Estimates for parametric Marcinkiewicz integrals in BMO and Campanato spaces

In this paper, the authors consider the behaviors of a class of parametric Marcinkiewicz integrals μ _Ω ^ρ , μ _Ω,λ ^*,ρ and μ _Ω,S ^ρ on BMO(ℝ ⁿ ) and Campanato spaces with complex parameter ρ and the kernel Ω in Llog⁺ L(S ⁿ⁻¹). Here μ _Ω,λ ^*,ρ and μ _Ω,S ^ρ are parametric Marcinkiewicz functions corresponding to the Littlewood-Paley g _λ *-function and the Lusin area function S, respectively. Under certain weak regularity condition on Ω, the authors prove that if f belongs to BMO(ℝ ⁿ ) or to a certain Campanato space, then [μ _Ω,λ ^*,ρ (f)]², [μ _Ω,S ^ρ (f)]² and [μ _Ω ^ρ (f)]² are either infinite everywhere or finite almost everywhere, and in the latter case, some kind of boundedness are also established.     

弱Hardy空间上的参数型Marcinkiewicz积分(英文)

证明了参数型Marcinkiewicz积分μρΩ是(Hp,∞,Lp,∞)(0相似文献   

弱Hardy空间上的参数型Marcinkiewicz积分

证明了参数型Marcinkiewicz积分μΩ^p是（H^p,∞ , L^p,∞）（0〈p≤1）型的算子，这里Ω是满足Lipα条件的R^＊上的零次齐次函数．对于p=1，减弱了Ω的条件μΩ^p得到μΩ^p是（H^1,∞ , L^1,∞）型的．作为上述结果的推论，得到了μΩ^p是弱（1，1）型的算子．     

带粗糙核的Marcinkiewicz积分算子在Herz空间的有界性

本文考虑如下的Macinkiewicz积分算子μΩ（f）（x）{∫0^∞｜FΩ ,t（x）｜^2t^-3dt}^1/2,其中FΩ ,t（x）=∫｜x-y｜≤tΩ （x-y）｜x-y｜^-n＋2f（y）dy在一定的条件下证明它是在Herz空间Kq^α,q上有界同时也是从Herz空间K1^α,p到弱Herz空间WK1^α,p上有界。     

On rough Marcinkiewicz integrals along surfaces

In this paper, the authors establish the LP-mapping properties of certain classes of Marcinkiewicz integral operators along surfaces with rough kernels. The results in this paper essentially extend as well as improve previously known results.     

Singular integrals with rough kernels along real-analytic submanifolds in

mapping properties will be established in this paper for singular Radon transforms with rough kernels defined by translates of a real-analytic submanifold in .

     

几类具有粗糙核的算子在加权Morrey空间上的有界性

设Ω∈L~q(S~(n-1))且1相似文献   

A note on the generalized Marcinkiewicz integral operators with rough kernels

In this paper,we study the generalized Marcinkiewicz integral operators MΩ,r on the product space Rn×Rm.Under the condition that Ω is a function in certain block spaces,which is optimal in some senses,the boundedness of such operators from Triebel-Lizorkin spaces to Lp spaces is obtained.