有界核Marcinkiewicz积分的弱型估计(英文) 被引量：3

WEAK-TYPE ESTIMATES FOR MARCINKIEWICZ INTEGRAL WITH BOUNDED KERNEL

在线阅读下载PDF

导出

摘要证明了Marcinkiewicz积分 μΩ 是 (H1,∞ ,L1,∞)型和弱 (1,1)型的算子 .这里核函数Ω零次齐次且满足消失条件和dini条件。 We prove that Marcinkiewicz integral μ_Ω is an operator of type (H^(1,∞),L^(1,∞)) and of weak type (1,1). Where kernel Ω∈L~∞(S^(n-1)) be a homogeneous function of degree zero satisfying the cancellation property and a certain dini-type condition introduced by Lee and Rim recently.=

作者瞿萌束立生

机构地区安徽师范大学数学与计算机科学学院

出处《安徽师范大学学报（自然科学版）》 CAS 2005年第1期10-13,共4页 Journal of Anhui Normal University(Natural Science)

基金 NSFofChina(10 3 710 87) EducationCommitteeofAnhuiProvince(2 0 0 3KJ0 3 4ZD)

关键词 MARCINKIEWICZ积分有界 DINI条件算子估计证明核函数消失 Marcinkiewicz integral weak Hardy space dini-type condition

分类号 O174.2 [理学—基础数学] O177 [理学—基础数学]

引文网络
相关文献

参考文献1

1Yong Ding Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China Dashan Fan Department of Mathematics, Anhui University and University of Wisconsin-Milwaukee. MW 53201 USA Yibiao Pan Department of Mathematics, University of Pittsburgh. Pittsburgh. Pennsylvania 15260. USA.L^p-Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels[J].Acta Mathematica Sinica,English Series,2000,16(4):593-600. 被引量：89

二级参考文献1

1徐靖南,朱维申,白世伟.压剪应力作用下多裂隙岩体的力学特性——本构模型[J].岩土力学,1993,14(4):1-15. 被引量：22

共引文献88

1赵志云,牛耀明.带参数的抛物型Marcinkiewicz积分的L^2(R^n)有界性[J].内蒙古大学学报（自然科学版）,2012,43(2):113-117.
2CHEN YanPing,DING Yong.Commutators of Littlewood-Paley operators[J].Science China Mathematics,2009,52(11):2493-2505. 被引量：5
3DING Yong,LI Ran.An integral estimate of Bessel function and its application[J].Science China Mathematics,2008,51(5):897-906. 被引量：4
4姜丽亚,陈琼蕾.一类广义的Marcinkiewicz积分算子的有界性[J].高校应用数学学报（A辑）,2004,19(3):303-310. 被引量：1
5JiangLiya,JiaHouyu,XuHan.BOUNDEDNESS OF GENERALIZED MARCINKIEWICZ INTEGRAL ON THE H^p-SOBOLEV SPACES[J].Applied Mathematics(A Journal of Chinese Universities),2004,19(4):399-404.
6LuShanzhen XuLifang.BOUNDEDNESS OF COMMUTATORS RELATED TO MARCINKIEWICZ INTEGRALS ON HARDY TYPE SPACES[J].Analysis in Theory and Applications,2004,20(3):215-230. 被引量：5
7陈冬香,陈杰诚.具有齐性核Marcinkiewicz积分交换子的Lipschitz估计[J].数学年刊（A辑）,2005,26(3):325-332. 被引量：3
8陆秋艳.Marcinkiewicz积分交换子的端点估计[J].哈尔滨师范大学自然科学学报,2011,27(4):26-29.
9陈冬香,陈杰诚.带粗糙核的Marcinkiewicz积分算子在Herz空间的有界性(英文)[J].数学进展,2005,34(5):591-599. 被引量：18
10张璞,胡晓敏.Marcinkiewicz积分交换子的研究进展[J].浙江理工大学学报（自然科学版）,2005,22(4):388-391.

同被引文献21

1DING Yong, LU Shanzhen & ZHANG PuDepartment of Mathematics, Beijing Normal University, Beijing 100875, China,Department of Information and Computing Science, Zhejiang Institute of Science and Technology, Hangzhou 310033, China.Weighted weak type estimates for commutators of the Marcinkiewicz integrals[J].Science China Mathematics,2004,47(1):83-95. 被引量：25
2陈冬香,陈杰诚.具有齐性核Marcinkiewicz积分交换子的Lipschitz估计[J].数学年刊（A辑）,2005,26(3):325-332. 被引量：3
3HORMANDER L. Translation invariant operators[J]. Acta Math, 1960, 104:93- 139.
4SAKAMOTO M, YABUTA K. Boundedncess of Marcinkiewicz functions[J]. Studia Math, 1999,135 : 103 - 142.
5DING Yong, LIN Qin-cheng, SHAO Shuang-lin. On the Marcinklewicz integral with variable kernels[J]. Indiana Univ Math J, 2004,53 (3) 805 - 821.
6XUE Qing-ying, YABUTA K. L^2-Boundendness of Marcinkewicz integrals along surfaces with variable kernels[J]. Sci Math Japonicae Online, 2006, e:269.
7DING Yong, LU Shan-zhen, SHAO Shuang-lin. Integral operators with kernels on weak Hardy spaces [J]. Mathematical Analysis and Applications, 2006,317:127 - 135.
8Stein E M.On the function of littlewood-paley,lusin and Marcinkiewicz[J].Trans.Amer.Math Soc,1958,88:430-466.
9Jeasung Lee,Kyung Soo Rim.Estimates of Marcinkiewicz integral with bounded homogeneous kerels of degree zero[J].Integral Equations and Operator Theory,2004,48:213-223.
10Cruz-uribe D,SFO,C perez.Two-weight,weak-type norm ineqralities for fractional integrals,Calderón-Zygmund operators and commutators[J].Indiana University Mathenatics Journal,2000,49:697-721.

引证文献3

1左大伟,贾慧羡.有界核Marcinkiewicz积分交换子的双权弱型不等式[J].石家庄铁道学院学报,2007,20(1):64-68.
2贾慧羡,吴世旭,左大伟.有界核的Marcinkiewicz积分交换子的一个有界性结果[J].石家庄铁道学院学报,2007,20(3):85-88.
3孙爱文,束立生.带变量核参数型Marcinkiewicz积分算子在Hardy空间的连续性[J].安徽师范大学学报（自然科学版）,2010,33(6):511-514.

1默会霞,陆善镇.带变量核的广义高阶Marcinkiewicz积分交换子在Herz型Hardy空间的有界性[J].数学物理学报（A辑）,2015,35(1):56-67.
2Yulan Jiao.AN ENDPOINT ESTIMATE FOR MAXIMAL MULTILINEAR SINGULAR INTEGRAL OPERATORS[J].Analysis in Theory and Applications,2007,23(4):307-314.
3陈琼蕾.关于一类奇异积分算子的加权有界性[J].浙江大学学报（理学版）,2004,31(5):481-483.
4全玉霞,高文华,江寅生.θ(t)型C-Z算子在非倍测度下的有界性[J].伊犁师范学院学报（自然科学版）,2010,4(3):6-10.
5吴伟.免保养直线滑动轴承“RJMP”[J].包装与食品机械,2009,27(6):81-81.
6甘大旺.运用《九章算术》的盈与不足思想速求均值与方差[J].高中数理化,2016,0(13):33-34.
7胡卫国,刘祥林,张攀峰,赵凤嫒,焦春美,魏鸿源,张日清,吴洁君,丛光伟,潘毅.A Comparison between AIN Films Grown by MOCVD Using Dimethylethylamine Alane and Trimethylaluminium as the Aluminium Precursors[J].Chinese Physics Letters,2007,24(2):516-519.
8魏杰.黑莓峰回路转[J].互联网周刊,2007(15):32-33.
9徐忠昌.从次亚紧到次仿紧与仿紧[J].南京大学学报（数学半年刊）,2001,18(2):244-250.
10科学家提出BEG和多层石墨烯（3-5）表面Cs原子超晶格的形成机制[J].中国科学院院刊,2012,27(5):623-623.

安徽师范大学学报（自然科学版）

2005年第1期

浏览历史

内容加载中请稍等...