[1]林燕,范超.一类线性算子的有界性探讨[J].江西师范大学学报(自然科学版),2015,(05):522-525.
　LIN Yan,FAN Chao.The Boundedness of a Class of Linear Operators[J].Journal of Jiangxi Normal University:Natural Science Edition,2015,(05):522-525.
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一类线性算子的有界性探讨()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2015年05期
页码:
522-525
栏目:
出版日期:
2015-10-01

文章信息/Info

Title:
The Boundedness of a Class of Linear Operators
作者:
林燕；范超
中国矿业大学 北京 理学院,北京,100083
Author(s):
LIN Yan；FAN Chao
关键词:
Toeplitz型算子; 有界性; Calderón-Zygmund型算子; BMO函数
Keywords:
Toeplitz operator; boundedness; Calderón-Zygmund type operator; BMO function
分类号:
O174.2；G642
文献标志码:
A
摘要:
研究1类在调和分析与复分析领域中有着重要应用的线性算子—Toeplitz 型算子，建立了由Calderón-Zygmund型算子与BMO函数生成的Toeplitz型算子的sharp极大估计，并由此得到了该类 To-eplitz型算子在 Lebesgue空间的有界性。
Abstract:
A class of linear operators called Toeplitz operators is studied,which have important applications in har-monic analysis and complex analysis. The sharp maximal estimates for the Toeplitz operators generated by Calderón-Zygmund type operators and BMO functions are established. And based on the sharp maximal estimates,the bound-edness of this kind of Toeplitz operators on Lebesgue spaces is obtained.

参考文献/References:

[1] 程其襄,张奠宙,魏国强,等.实变函数与泛函分析基础 [M].3版.北京:高等教育出版社,2010.
[2] 周美珂.泛函分析 [M].2版.北京:北京师范大学出版社,2007.
[3] 张恭庆,林源渠.泛函分析讲义:上册 [M].北京:北京大学出版社,2001.
[4] Folland G B.Real analysis:Modern techniques and their applications [M].2版.北京:世界图书出版公司北京公司,2007.
[5] Coifman R R,Rochberg R,Weiss G.Factorization theorems for Hardy spaces in several variables [J].Ann Math,1976,103(3):611-635.
[6] Chiarenza F,Frasca M,Longo P.W-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients [J].Trans Amer Math Soc,1993,336(2):841-853.
[7] Di Fazio G,Ragusa M A.Interior estimates in Morrey spaces for strongly solutions to nondivergence form equations with discontinuous coefficients [J].J Funct Anal,1993,112(2):241-256.
[8] Paluszynski M.Characterization of the Besov spaces via the commutator operator of Coifman,Rochberg and Weiss [J].Indiana Univ Math J,1995,44(1):1-17.
[9] Chang Derchen,Li Junfeng.Weighted scale estimates for generalized Calderón-Zygmund type operator [J].Contemporary Math Amer Math Soc,2007,44(5):61-70.
[10] Krantz S G,Li Songying.Boundedness and compactness of integral operators on spaces of homogeneous type and applications,I [J].J Math Anal Appl,2001,258(2):629-641.
[11] 邱道文.齐型空间上的一类积分算子 [J].数学年刊:A辑,2001,22(6):797-804.
[12] Lin Yan,Lu Shanzhen.Toeplitz operators related to strongly singular Calderón-Zygmund opetators [J].Sci China Ser A,2006,49(8):1048-1064.
[13] Lin Yan.Endpoint estimates for Calderón-Zygmund type operators [J].Acta Math Sinica English Ser,2010,26(3):523-532.
[14] 林燕.Calderón-Zygmund型算子及其交换子的sharp极大函数估计 [J].数学物理学报,2011,31A(1):206-215.
[15] Lin Yan,Sun Guofeng.Generalized Calderón-Zygmund operators and commutators on weighted Morrey spaces [J].PanAmer Math J,2015,25(1):53-65.
[16] Stein E M.Harmonic analysis:real-variable methods,orthogonality,and oscillatory integrals [M].Princeton:Princeton Univ Press,1993.

备注/Memo

备注/Memo:
国家自然科学基金(11171345)；中央高校基本科研业务费(2009QS16)；北京高等学校青年英才计划(YETP0946)
更新日期/Last Update: 1900-01-01