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   

沿复合曲线的粗糙核参数型Marcinkiewicz积分算子的有界性

研究沿复合曲线的粗糙核参数型Marcinkiewicz积分算子,在积分核满足相当弱的尺寸条件下,建立了这些算子的L~p有界性.作为应用,相应于面积积分和Littlewood-Paley-g_λ~*函数的参数型Marcinkiewicz积分算子的L~p有界性也被给出.     

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.     

积域上粗糙核Marcinkiewicz积分的L~p有界性

本文证明了积域上的Ｍａｒｃｉｎｋｉｅｗｉｃｚ积分算子μΩ是Ｌｐ（ＲｎｘＲｍ）（１＜ｐ＜∞）有界的．这里核函数Ω仅满足尺寸条件．即Ω∈Ｌｐ（Ｓｎ－１×Ｓｍ－１）（ｑ＞１）,而不需添加任何光滑性条件．本文结果可视为 Ｓｔｅｉｎ结果的一个改进．     

积域上粗糙核Marcinkiewicz积分的Lp有界性

本文证明了积域上的Marcinkiewicz积分算子μΩ是Lp( Rn× Rm) (11),而不需添加任何光滑性条件. 本文结果可视为Stein结果的一个改进.     

带粗糙核的多线性振荡奇异积分

本文考虑多线性算子ＴＡｆ（ｘ）＝∫ＲｎｅｉＰ（ｘ，ｙ）Ω（ｘ－ｙ）｜ｘ－ｙ｜ｎ＋ｍＲｍ＋１（Ａ；ｘ，ｙ）ｆ（ｙ）ｄｙ，ｎ２，其中Ｐ（ｘ，ｙ）是Ｒｎ×Ｒｎ中的实值多项式，Ω是零次齐次函数且满足ｍ阶消失性条件，Ｒｍ＋１（Ａ；ｘ，ｙ）＝Ａ（ｘ）－｜α｜ｍＤαＡ（ｙ）（ｘ－ｙ）α，对任何｜α｜＝ｍ，ＤαＡ∈ＢＭＯ（Ｒｎ）．证明了Ω∈Ｌｑ（Ｓｎ－１）且ｑ＞１时，对任何１＜ｐ＜∞，‖ＴＡｆ‖ｐＣ（ｎ，ｍ，ｐ，ｄｅｇＰ）｜α｜＝ｍ‖ＤαＡ‖ＢＭＯ‖ｆ‖ｐ     

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。     

各向异性极大算子及它们的应用

本文证明了一类与异性伸缩相关的极大算子在Ｌ＾ｐ（Ｒ＾ｎ）上是有界的，其中１〈ｐ≤∝，ｎ≥２。进一步，作为应用我们建立了算子Ｔｆ（ｘ）＝ｓｕｐε〉０│Ｔεｆ（ｘ）│Ｌ＾ｐ有界性，其中Ｔε是带有变化核的奇异积分。     

粗糙平方函数及极大算子的弱型估计

§ 1　 PreliminariesWe considerψ( x)∈ L1 ( Rn) satisfying the mean valuezero,i.e.∫Rnψdx=0 ,and definethe square function g( f) on Rnbyg( f) ( x) =( k|ψk* f|2 ) 1 2 ( x)for f∈ S( Rn) ,the Schwartz space,whereψk( x) =ψ2 k( x) .　　 Whenψ has some smooth property,one can obtain the weak type estimate by viewingthe square function g( f) as the vector-valued singularintegrals,which the readercan referto [1 ,2 ] .As for the results aboutthe Lp-estimates,see [3,4 ] .In this paper,we sha…     

沿旋转曲面奇异积分的有界性

本文建立了具有粗糙核的沿曲面奇异积分算子的L^P有界性．其中粗糙核K(y)=Ω（y)/|y|^n,y∈R^n以及曲面{(y，φ(|y|）)：y∈R^n)满足某种光滑条件．同时，相应极大算子的有界性也被得到.     

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.     

A Note on Rough Parametric Marcinkiewicz Functions

In this note, we obtain sharp L~p estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L~1(S~(n-1)).     

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.     

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.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates of rough maximal functions along surfaces with applications

In this paper, we study the L^p mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the L^p boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(S^n-1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.     

粗糙核抛物型奇异积分算子与外插——献给陆善镇教授75华诞

本文研究粗糙核抛物型奇异积分算子及其极大算子.借助精细的Fourier变换估计和LittlewoodPaley理论,并结合外插讨论,在积分核满足球面Hardy函数条件和相当弱的径向尺寸条件下,本文建立这些算子的L^p有界性.进一步,关于沿一般光滑曲面的奇异积分算子及其极大算子的相应结果也被建立.这些结果即使在迷向情形也是新的.     

有限型流形上的粗糙奇异积分

探讨了沿有限型曲面的粗糙奇异积分算子在Triebel-Lizorkin空间和Besov空间上的有界性,建立了该算子的l~q值不等式.     

A Class of Maximal Functions with Oscillating Kernels

The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted.     

Rough multiple singular integrals along hypersurfaces

In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)ε(Sm-1 × Sn-1) (ε = 1 or 2) supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq(R3) for all q > 1. The condition on the integral kernels is known to be optimal.