摘要在多线性Calderón-Zygmund算子T的最小非退化假设条件下，本文给出了一类交换子Tbj的Lp1×…×Lpm → Lq有界性的刻画.这一结果将Hytönen关于线性交换子的部分结果推广到多线性情形.
| | 服务 | |  | 加入引用管理器 | | E-mail Alert | | RSS | | 收稿日期: 2018-11-22 | | 基金资助:国家自然科学基金资助项目（11871096）
| | 作者简介: 瞿萌,E-mail:qumeng@mail.ahnu.edu.cn;方小珍,E-mail:fxz9511@126.com;王敏,E-mail:ymz1121@163.com |
[1] Chaffee L., Characterization of BMO through commutators of bilinear singular integral operators, Proc. Amer. Math. Soc., 1999, 127(1):79-87.
[2] Chaffee L., Cruz-Uribe D., Necessary conditions for the boundedness of linear and bilinear commutators on Banach function spaces, Math. Inequal. Appl., 2017, 21(1):1-16.
[3] Christ M., Journé J., Polynomial growth estimates for multilinear singular integral operators, Acta Math., 1987, 159(1):51-80.
[4] Fabes E., Jerison D., Kenig C., Multilinear Littlewood-Paley estimates with applications to partial differential equations, Proc. Natl. Acad. Sci., 1982, 79(18):5746-5750.
[5] Fabes E., Jerison D., Kenig C., Multilinear square functions and partial differential equations, Amer. J. Math., 1985, 107(6):1325-1368.
[6] Grafakos L., Torres R., Multilinear Calderón-Zygmund theory, Adv. Math., 2002, 165:124-164.
[7] Guo W. C., Lian J. L., Wu H. X., The unified theory for the necessity of bounded commutators and applications, J. Geom. Anal., 2020, 30(4):3995-4035.
[8] Huang Z., Huang A. W., Xu J. S., Multilinear commutators of multilinear singular integrals with Lipschitz functions (in Chinese), J. Mathematics, 2011, 31(4):738-748.
[9] Hytönen T. P., The Lp-to-Lq boundedness of commutators with applications to the Jacobian operator, arXiv:1804.11167.
[10] Lerner A., Ombrosi S., Pérez C., et al., New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory, Adv. Math., 2009, 220(1):1222-1264.
[11] Li L., Ma B. L., Zhou J., Multilinear Calderón-Zygmund operators on Morrey space with non-doubling measures, Publ. Math. Debrecen, 2011, 78(2):283-296.
[12] Li Z. Y., Xue Q. Y., Endpoint estimates for the commutators of multilinear Calderón-Zygmund operators with Dini type kernels, J. Inequal. Appl., 2016, No. 252, 22 pp.
[13] Lin Y., Zhang N., Sharp maximal and weighted estimates for multilinear iterated commutators of multilinear integrals with generalized kernels, J. Inequal. Appl., 2017, No. 276, 15 pp.
[14] Liu F., Wu H. X., Zhang D. Q., On the multilinear singular integrals and commutators in the weighted amalgam spaces, J. Funct. Spaces, 2014, Art. ID686l7, 12 pp.
[15] Lu G., Zhang P., Multilinear Calderón-Zygmund operators with kernels of Dini's type and applications, Nonlinear Anal., 2014, 107:92-117.
[16] Maldonado D., Naibo V., Weighted norm inequalities for paraproducts and bilinear pseudodifferential operators with mild regularity, J. Fourier Anal. Appl., 2009, 15:218-261.
[17] Mo H. X., Lu S. Z., Commutators generated by multilinear Calderón-Zygmund type singular integral and Lipschitz function, Acta Math. Appl. Sin. Engl. Ser., 2014, 30(4):903-912.
[18] Pérez C., Torres R., Sharp maximal function estimates for multilinear singular integrals, Contemp. Math., 2003, 320:323-331.
[19] Si Z. Y., Xue Q. Y., A note on vector-valued maximal multilinear operators and their commutators, Math. Inequal. Appl., 2016, 19(1):249-262.
[20] Sun Y. L., Zhao P. F., The boundedness of commutator of multilinear singular integral operator of Calderón-Zygmund (in Chinese), Natural Science J. of Harbin Norm. Univ., 2009, 6:23-26.
[21] Wang P. W., Liu Z. G., Weighted norm inequalities for multilinear Calderón-Zygmund operators in generalized Morrey spaces, J. Inequal. Appl., 2017, No. 48, 10 pp.
[22] Wang W., Xu J. S., Commutators of multilinear singular integrals operators with Lipschitz function, Commun. Math. Res., 2009, 25(4):318-328.
[23] Xu J. S., Multilinear commutators of multilinear singular integrals, Acta Math. Sinica, Chinese Series, 2008, 51(5):1021-1035.
[24] Xue Q. Y., Yan J. Q., Generalized commutators of multilinear Calderón-Zygmund type operators, J. Math. Soc. Japan, 2016, 68(3):1161-1188.
[25] Zhou X. S., Huang C. X., Hu H. J., Inequality estimates for the boundedness of multilinear singular and fractional integral operators, J. Inequal. Appl., 2013, No. 303, 15 pp.
|
| [1] | 安润玲, 高永兰. C*-代数上强保k-skew交换性的映射[J]. 数学学报, 2021, 64(4): 545-550. | | [2] | 王盛荣, 徐景实. 加权变指标Herz-Morrey空间上的双线性Hardy算子的交换子[J]. 数学学报, 2021, 64(1): 123-138. | | [3] | 李亚涛. Sobolev空间中非电阻MHD方程局部适定性[J]. 数学学报, 2020, 63(4): 335-348. | | [4] | 郭庆栋, 周疆. 一些算子的交换子在广义Morrey空间上的紧性[J]. 数学学报, 2020, 63(4): 367-380. | | [5] | 陶双平, 逯光辉. Morrey空间上Marcinkiewicz积分与R[J]. 数学学报, 2019, 62(2): 269-278. | | [6] | 王定怀, 刘宗光, 周疆, 滕志东. 变指标中心BMO空间[J]. 数学学报, 2018, 61(4): 641-650. | | [7] | 王定怀, 周疆. 一类新型BMO空间[J]. 数学学报, 2017, 60(5): 833-846. | | [8] | 张蕾, 石少广, 郑庆玉. 含参数加权极大Lebesgue空间中次线性算子的有界性质[J]. 数学学报, 2017, 60(3): 521-530. | | [9] | 王玮, 侯晋川. 自伴标准算子代数上强保持k-斜交换性映射的刻画[J]. 数学学报, 2017, 60(1): 39-52. | | [10] | 毛素珍, 孙丽静, 伍火熊. 双线性Fourier乘子交换子的有界性与紧性[J]. 数学学报, 2016, 59(3): 317-334. | | [11] | 梅婷, 丁勇, 马柏林. 多线性算子族的α-Carleson测度[J]. Acta Mathematica Sinica, English Series, 2015, 58(4): 593-600. | | [12] | 李立莉. 单群2G2(32n+1)的拟刻画[J]. Acta Mathematica Sinica, English Series, 2015, 58(3): 359-364. | | [13] | 束立生, 王敏, 瞿萌. 变指数Herz空间上的Hardy型算子的交换子[J]. Acta Mathematica Sinica, English Series, 2015, 58(1): 29-40. | | [14] | 陈艳萍, 韩寒. Hardy-Littlewood极大算子的交换子的尖锐加权模不等式[J]. Acta Mathematica Sinica, English Series, 2014, 57(3): 445-452. | | [15] | 陶双平, 任转喜. n维Hausdorff交换子的加权估计[J]. Acta Mathematica Sinica, English Series, 2014, 57(2): 351-364. |
|
PDF全文下载地址:
http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23803
圆环的加正规权Bergman空间上正符号Toeplitz算子何忠华1,夏锦2,王晓峰21.广东金融学院金融数学与统计学院广州510521;2.广州大学数学与信息科学学院广州510006PositiveToeplitzOperatorsonBergmanSpaceofAnnularInducedbyR ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27Frchet空间上集值微分方程初值问题解的高阶收敛性王培光,邢珍钰,吴曦冉河北大学数学与信息科学学院保定071002Higher-OrderConvergenceofSolutionsofInitialValueProblemforSetDifferentialEquationsin ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27Banach空间中正则非退化异宿环的Lipschitz扰动陈员龙,骆世广广东金融学院金融数学与统计学院广州510521TheLipschitzPerturbationsofRegularNondegenrateHeteroclinicCyclesinBanachSpacesYuanLongCHEN, ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27半序MengerPM-空间中广义弱压缩映射的最佳逼近点定理吴照奇1,朱传喜1,袁成桂21.南昌大学理学院数学系南昌330031;2.英国斯旺西大学数学系斯旺西SA28PPBestProximityPointTheoremsforGeneralizedWeakContractiveMappingsin ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27完备度量空间中的混沌判定吴小英,陈员龙,王芬广东金融学院金融数学与统计学院广州510521ChaoticCriteriainCompleteMetricSpacesXiaoYingWU,YuanLong,CHENFenWANGSchoolofFinancialMathematicsandStatis ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27空间几何常数与集值非扩张映射的不动点左占飞重庆三峡学院数学与统计学院重庆404100SomeGeometricConstantsandFixedPointsforMultivaluedNonexpansiveMappingsZhanFeiZUODepartmentofMathematicsandSt ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27Banach空间上p-fusion框架的若干等价描述林丽琼1,张云南21.福州大学数学与计算机科学学院福州350108;2.福建师范大学数学与信息学院福州350108SomeEquivalentDescriptionsofp-fusionFramesonBanachSpacesLiQiongLIN1 ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27加权变指标Herz-Morrey空间上的双线性Hardy算子的交换子王盛荣,徐景实桂林电子科技大学数学与计算科学学院桂林541004CommutatorsofBilinearHardyOperatorsonWeightedHerzMorreySpaceswithVariableExpo ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27加权Bloch空间上复合算子的线性组合张利,楚秀娇南阳师范学院南阳473061LinearCombinationsofCompositionOperatorsonWeightedBlochTypeSpaceLiZHANG,XiuJiaoCHUNanyangNormalUniversity,Nanya ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27bp(2)空间中的等距映射王瑞东,王普天津理工大学理学院天津300384TheIsometryonbp(2)SpaceRuiDongWANG,PuWANGDepartmentofMathematics,TianjinUniversityofTechnology,Tianjin300384,P.R.C ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27
|
