共查询到20条相似文献,搜索用时 156 毫秒
1.
In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results. 相似文献
2.
We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory integrals with polynomial phase. By using
these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals
under very weak size conditions on the kernel functions. 相似文献
3.
在F-粗积分、■-粗积分定义的基础上研究了F-粗积分与■-粗积分之间的关系及粗变化度与粗萎缩度和粗扩充度、粗变化率与粗萎缩率和粗扩充率的关系。 相似文献
4.
The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic. 相似文献
5.
证明了一组次线性算子及其交换子,如具有粗糙核的Calderón-Zygmund算子、Ricci-Stein振荡奇异积分、Marcinkiewicz积分、分数次积分和振荡分数次积分及其交换子,在一类广义Morrey空间上的有界性.作为应用得到了非散度型椭圆方程在上述Morrey空间的内部正则性. 相似文献
6.
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. 相似文献
7.
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. 相似文献
8.
Yueshan Wang 《分析论及其应用》2017,33(2)
Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds,the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases,we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control,then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces. 相似文献
9.
The authors establish the boundedness on homogeneous weighted Herz spaces for a large class of rough grals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered. 相似文献
10.
11.
Ferit G"{U}RB"{U}Z 《数学年刊B辑(英文版)》2020,41(1):77-98
Let L =-?+V(x) be a Schr?dinger operator, where ? is the Laplacian on ■~n,while nonnegative potential V(x) belonging to the reverse H?lder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schr?dinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples. 相似文献
12.
Abstract
In this paper, we study multilinear oscillatory singular integrals with rough kernel, and give a criterion of certain boundedness
for this kind of operator
Research supported by NNSF of China (No.19131080) and NEDF of China 相似文献
13.
Shanzhen Lu 《Frontiers of Mathematics in China》2007,2(1):61-72
This paper is a survey on the theory and application of some block spaces on the unit sphere introduced by Jiang and the author
of this paper in the study of singular integrals and some related operators with rough kernels.
相似文献
14.
Singular integrals and commutators on homogeneous groups 总被引:2,自引:0,他引:2
Let G be a homogeneous group. In this paper, the authors establish several general theorems for the boundedness of sublinear operators and commutators generated by linear operators and BMO(G)functions on the weighted Lebesgue space on G. The conditions of these theorems are satisfied by many important operators in analysis and these operators satisfy only some weak conditions on the size of operators and are known to be bounded in the unweighted case. Some of these theorems are best possible even when G is the Euclidean space. The authors also give some applications of their theorems to the boundedness on weighted spaces of rough singular integrals, oscillatory integrals, parabolic singular integrals, their commutators and the maximal operators associated with them. 相似文献
15.
Nicolas Th. Varopoulos 《Milan Journal of Mathematics》2008,76(1):419-429
In this note I give an extension of the T1-Theorem of David and Journé. In this extension the standard estimates on the kernel
are replaced by “average standard estimates” but the classical proof is essentially identical. I then use that extension to
prove the Lp-boundedness of some natural rough singular integrals. The applications of these singular integrals in Potential Theory has
already been described in my previous paper in the area.
Received: September 2008 相似文献
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17.
In this paper, we establish the Lp(Rn+1) boundedness for the commutators of singular integrals associated to surfaces of revolution, {(t, φ(|t|)):t∈Rn}, with rough kernels ? ∈ L(log L)2(Sn-1), if φ(|t|) = |t|. 相似文献
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19.
Juan Carlos Sampedro 《The Ramanujan Journal》2016,40(3):541-555
In this article, we prove some identities which allow us to evaluate some multiple unit square integrals. In our examples, we will give the value of some double and triple integrals. We then prove several classical integral formulas with the help of these identities and present others that seem to be new. Finally, we get double integrals for classical constants and different expressions for two Ramanujan’s integral formulas. 相似文献