数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1306-1319.
收稿日期:
2022-01-17
出版日期:
2022-10-26
发布日期:
2022-09-30
通讯作者:
张学军
E-mail:xuejunttt@263.net
基金资助:
Received:
2022-01-17
Online:
2022-10-26
Published:
2022-09-30
Contact:
Xuejun Zhang
E-mail:xuejunttt@263.net
Supported by:
摘要:
该文讨论了正规权一般函数空间到一种特殊的正规权Bloch型空间之间复合算子的有界性和紧性, 作者就所有情形给出了充要条件.
中图分类号:
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.
Yuting Guo,Xuejun Zhang. Composition Operators from Normal Weight General Function Spaces to Bloch Type Spaces[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1306-1319.
1 | Zhao R H . On a general family of function spaces. Ann Acad Sci Fenn Math Diss, 1996, 105, 1- 56 |
2 |
Zhang X J , He C Z , Cao F F . The equivalent norms of F(p, q, s) space in $\mathbb{C}^n$. J Math Anal Appl, 2013, 401, 601- 610
doi: 10.1016/j.jmaa.2012.12.032 |
3 | Jiang L J , He Y Z . Composition operators from $\beta^\alpha$ to $F(p, q, s).$. Acta Math Sci, 2003, 23B (2): 252- 260 |
4 | 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, 2012, 19 (8): 899- 926 |
5 |
Shi J H , Luo L . Composition operators on the Bloch space of several complex variables. Acta Math Sin (English Series), 2000, 16, 85- 98
doi: 10.1007/s101149900028 |
6 |
Ye S L . Weighted composition operators from $F(p, q, s)$ into logarithmic Bloch space. J Kore Math Soc, 2008, 45 (4): 977- 991
doi: 10.4134/JKMS.2008.45.4.977 |
7 | Yang W F . Volterra composition operators from $F(p, q, s)$ spaces to Bloch-type spaces. Bull Malay Math Sci, 2011, 34 (2): 267- 277 |
8 |
Liang Y X . On an integral-type operator from a weighted-type space to $F(p, q, s)$ on the unit ball. Complex Var Ellip Equ, 2015, 60 (2): 282- 291
doi: 10.1080/17476933.2014.926338 |
9 |
Wulan H S . Compactness of the composition operators from the Bloch space B to $Q_{k}$ spaces. Acta Math Sin (English Series), 2005, 21, 1415- 1424
doi: 10.1007/s10114-005-0584-7 |
10 |
Zhang X J , Guo Y T , Shang Q L , Li S L . The Gleason's problem on $F(p, q, s)$ type spaces in the unit ball of $\mathbb{C}^n$. Complex Anal Oper Theory, 2018, 12 (5): 1251- 1265
doi: 10.1007/s11785-017-0743-8 |
11 |
Zhang X J , Xu S , Li S L , Xiao J B . Composition operators on $F(p, q, s)$ type spaces in the unit ball of $\mathbb{C}^n$. Complex Anal Oper Theory, 2018, 12 (1): 141- 154
doi: 10.1007/s11785-016-0610-z |
12 | Li S L , Zhang X J , Xu S . The equivalent characterization of $F(p, q, s)$ space on bounded symmetric domains of $\mathbb{C}^n$. Acta Math Sci, 2017, 37B (6): 1791- 1802 |
13 |
Li S X , Stević S . Generalized composition operators on Zygmund spaces and Bloch type spaces. J Math Anal Appl, 2008, 338, 1282- 1295
doi: 10.1016/j.jmaa.2007.06.013 |
14 | Xiao J . Composition operators associated with Bloch-type spaces. Complex Var Theory Appl, 2001, 46 (2): 109- 121 |
15 | Wulan H S, Zhu K H. Möbius Invariant $Q_{K}$ Spaces. Swizerland: Springer-Nature, 2017 |
16 |
Chen H H , Gauthier P . Composition operators on $\mu$-Bloch spaces. Canad J Math, 2009, 61, 50- 75
doi: 10.4153/CJM-2009-003-1 |
17 | Zhang X J , Xi L H , Fan H X , Li J F . Atomic decomposition of $\mu$-Bergman space in $\mathbb{C}^n$. Acta Math Sci, 2014, 34B (3): 779- 789 |
18 | 张学军, 吕睿昕, 唐鹏程. $\mathbb{C}^n$中单位球上一般Hardy型空间的几种等价刻画. 数学年刊, 2019, 40A (2): 113- 126 |
Zhang X J , Lv R X , Tang P C . Several equivalent characterizations of general Hardy type spaces on the unit ball in $\mathbb{C}^n$. Chin Ann Math, 2019, 40A (2): 113- 126 | |
19 | Hu Z J . Composition operators between Bloch-type spaces in the polydisc. Sci in China, 2005, 48A (supp): 268- 282 |
20 |
Zhang X J , Xu S . Weighted differentiation composition operators between normal weight Zygmund spaces and Bloch spaces in the unit ball of $\mathbb{C}^n$ for $n>1$. Complex Anal Oper Theory, 2019, 13 (3): 859- 878
doi: 10.1007/s11785-018-0810-9 |
21 |
Li S L , Zhang X J . Composition operators on the normal weight Zygmund spaces in high dimensions. J Math Anal Appl, 2020, 487 (2): 124000
doi: 10.1016/j.jmaa.2020.124000 |
22 | 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 |
23 |
Zhang X J , Huang Y . Composition operator between normal weight Dirichlet type space and Bloch type space. Complex Var Ellipt Equ,
doi: 10.1080/17476933.2021.1934678 |
24 | Littlewood J . On inequalities in the theory of functions. Proc London Math Soc, 1925, 23 (2): 481- 519 |
25 |
Nordgren E . Composition operators. Canad J Math, 1968, 20, 442- 449
doi: 10.4153/CJM-1968-040-4 |
26 | Rudin W. Function Theory in the Unit Ball of $\mathbb{C}^n$. New York: Springer, 1980 |
27 | Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. New York: Springer (GTM 226), 2005 |
28 | Cowen C , MacCluer B . Composition Operators on Spaces of Analytic Functions. Boca Raton: CRC Press, 1995 |
29 |
Liu Y M , Yu Y Y . Weighted differentiation composition operators from mixed-norm to Zygmund spaces. Numer Funct Anal Optim, 2010, 31, 936- 954
doi: 10.1080/00268976.2010.505108 |
30 | Lou Z J . Composition operators on Bloch type spaces. Analysis, 2003, 23, 81- 95 |
31 | Wang M F . Weighted composition operators between Dirichlet spaces. Acta Math Sci, 2011, 31B (2): 641- 651 |
32 | 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 |
33 | Tang X M . Extended Cesàro operators between Bloch-type spaces in the unit ball of $\mathbb{C}^n$. J Math Anal Appl, 2007, 326 (2): 1199- 1211 |
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