$ \boldsymbol{H^{p,q,s}}({\Bbb D})$上的复合算子

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 1-13.

• • 下一篇

$ \boldsymbol{H^{p,q,s}}({\Bbb D})$上的复合算子

陈洪欣(),张学军^*(),周敏()

湖南师范大学数学与统计学院长沙410006

收稿日期:2022-05-02 修回日期:2022-08-05 出版日期:2023-02-26 发布日期:2023-03-07
通讯作者: 张学军 E-mail:1755310775@qq.com;xuejunttt@263.net;1479898554@qq.com
作者简介:陈洪欣, E-mail: 1755310775@qq.com|周敏, E-mail: 1479898554@qq.com
基金资助:
国家自然科学基金(11942109);湖南省自然科学基金(2022JJ30369)

Composition Operators on $ \boldsymbol{H^{p,q,s}}({\Bbb D})$

Chen Hongxin(),Zhang Xuejun^*(),Zhou Min()

College of Mathematics and Statistics, Hunan Normal University, Changsha 410006

Received:2022-05-02 Revised:2022-08-05 Online:2023-02-26 Published:2023-03-07
Contact: Xuejun Zhang E-mail:1755310775@qq.com;xuejunttt@263.net;1479898554@qq.com
Supported by:
The NSFC(11942109);The NSFH(2022JJ30369)

摘要/Abstract

摘要：

设 $\varphi$ 是复平面${\Bbb C}$中单位圆盘 ${\Bbb D}$上的解析自映射. 该文刻画了一般Hardy型空间$H^{p,q,s}({\Bbb D})$上使得复合算子$C_{\varphi}$有界或者紧时的符号函数 $\varphi$.

关键词: 复合算子, 有界性, 紧性, 一般 Hardy 型空间, 单位圆盘

Abstract:

Let $\varphi$ be an analytic self-map of the unit disc ${\Bbb D}$ in the complex plane ${\Bbb C}$. In this paper, the authors characterize those symbols $\varphi$ such that composition operators $C_{\varphi}$ are bounded or compact on the general Hardy type space $H^{p,q,s}({\Bbb D})$.

Key words: Composition operator, Boundedness, Compactness, General Hardy type space, Unit disc

中图分类号:

O174.56

陈洪欣,张学军,周敏. $ \boldsymbol{H^{p,q,s}}({\Bbb D})$上的复合算子[J]. 数学物理学报, 2023, 43(1): 1-13.

Chen Hongxin,Zhang Xuejun,Zhou Min. Composition Operators on $ \boldsymbol{H^{p,q,s}}({\Bbb D})$[J]. Acta mathematica scientia,Series A, 2023, 43(1): 1-13.

参考文献 17

[1]	Stević S, Ueki S I. Weighted composition operators from the weighted Bergman space to the weighted Hardy space on the unit ball. Appl Math Comput, 2010, 215: 3526-3533
[2]	Čučković Z, Zhao R H. Weighted composition operators between different weighted Bergman spaces and different Hardy spaces. IIlinois J of Math, 2007, 51(2): 479-498
[3]	Ueki S I, Luo L. Compact weighted composition operators and multiplication operators between Hardy spaces. Abstr Appl Anal, 2008, Article ID: 196498
[4]	Zhang X J, Lv R X, Tang P C. Several equivalent characterizations of general Hardy type spaces on the unit ball in $ {\Bbb C}^{\it n}$. Chin J Conte Math, 2019, 40(2): 101-114
[5]	Li S L, Zhang X J. Toeplitz type operator and Gleason's problem on $H^{p,q,s}(B)$ of ${\Bbb C}^{n}$. Complex Var Ellip Equat, 2021, 66(8): 1362-1379
[6]	Xu S, Zhang X J. Multiplier and composition operator between several holomorphic function spaces in ${{\Bbb C}^{\it n}}$. Complex Anal Oper Theory, 2021, 15(2), Article number: 36
[7]	Cowen C C, MacCluer B D. Composition Operators on Spaces of Analytic Functions. Boca Raton: CRC Press, 1995
[8]	Zhu K H. Operator Theory in Function Spaces. Providence, RI: Amer Math Soc, 2007
[9]	Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. New York: Springer-Verlag, 2005
[10]	Rudin W. Function Theory in the Unit Ball of ${\Bbb C}^n$. New York: Springer-Verlag, 1980
[11]	Shields A, Williams D. Bounded projections, duality and multipliers in space of analytic functions. Trans Amer Math Soc, 1971, 167: 253-268
[12]	Littlewood J. On inequalities in the theory of functions. Proc London Math Soc, 1925, 23(2): 481-519
[13]	Tang X M. Essential norms of weighted composition operators from Bloch-type space to $H^{\infty}$ on the unit ball. Complex Anal Oper Theory, 2015, 9(1): 229-244 doi: 10.1007/s11785-014-0410-2
[14]	Ye S L. Weighted composition operators from $F(p,q,s)$ into logarithmic Bloch space. J Kore Math Soc, 2008, 45(4): 977-991
[15]	Zhou Z H, Chen R Y. Weighted composition operator from $F(p,q,s)$ to Bloch type spaces on the unit ball. Int J Math, 2008, 19(8): 899-926 doi: 10.1142/S0129167X08004984
[16]	张学军, 李菊香. ${\Bbb C}^n$中单位球上$\mu$-Bloch空间之间的复合算子. 数学物理学报, 2009, 29A(3): 573-583
	Zhang X J, Li J X. Weighted composition operators between $\mu$-Bloch spaces on the unit ball of ${\Bbb C}^n$. Acta Math Sci, 2009, 29A(3): 573-583
[17]	Li S L, Zhang X J, Xu S. The compact composition operator on the $\mu$-Bergman space in the unit ball. Acta Math Sci, 2017, 37B(2): 425-438

$ \boldsymbol{H^{p,q,s}}({\Bbb D})$上的复合算子

Composition Operators on $ \boldsymbol{H^{p,q,s}}({\Bbb D})$

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献 17

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	李扬荣, 王凤玲, 杨爽. 带非线性噪音的随机${g}$-Navier-Stokes方程的后向弱紧均值动力学[J]. 数学物理学报, 2023, 43(2): 531-548.
[2]	李安然,樊丹丹,魏重庆. 临界零质量Kirchhoff型方程的解及其渐近行为[J]. 数学物理学报, 2022, 42(6): 1729-1743.
[3]	刘文杰,谢胜利. 脉冲无穷时滞中立型测度微分方程mild解的存在性[J]. 数学物理学报, 2022, 42(6): 1671-1681.
[4]	郭雨婷,张学军. 正规权一般函数空间到Bloch型空间的复合算子[J]. 数学物理学报, 2022, 42(5): 1306-1319.
[5]	许文丁,钟婷. 非光滑牛顿算法的收敛性[J]. 数学物理学报, 2022, 42(5): 1537-1550.
[6]	何泽荣,周楠. 具有年龄等级结构的种群竞争系统的最优收获控制[J]. 数学物理学报, 2022, 42(1): 228-244.
[7]	徐宁,周泽华,丁颖. 单位球Hardy空间上加权复合算子的交换子[J]. 数学物理学报, 2021, 41(6): 1606-1615.
[8]	贾哲,杨作东. 带非线性扩散项和信号产生项的趋化-趋触模型解的整体有界性[J]. 数学物理学报, 2021, 41(5): 1382-1395.
[9]	DestaLeta Temesgen,刘文军,丁建. 相对论简并量子等离子体中完全非线性重离子声波行波解的动力学研究[J]. 数学物理学报, 2021, 41(2): 496-506.
[10]	唐鹏程,徐思,张学军. Cⁿ中对数权一般函数空间上的Bergman型算子[J]. 数学物理学报, 2020, 40(5): 1151-1162.
[11]	赵艳辉,吴修云,廖春艳. 单位球上加权Bergman空间到Ƶ_μ型空间的加权Cesàro算子[J]. 数学物理学报, 2020, 40(3): 569-578.
[12]	韩瑶瑶,赵凯. Marcinkiewicz积分算子及其交换子在非齐度量测度空间上的有界性[J]. 数学物理学报, 2020, 40(3): 597-610.
[13]	苟海德. Banach空间阻尼弹性系统L-拟mild解的存在性[J]. 数学物理学报, 2020, 40(2): 408-421.
[14]	徐思,张学军. 单位球上正规权Zygmund空间上的加权复合算子[J]. 数学物理学报, 2020, 40(2): 288-303.
[15]	朱波,韩宝燕,刘立山. 一类混合型分数阶半线性积分-微分方程解的存在性[J]. 数学物理学报, 2019, 39(6): 1334-1341.