单位球上正规权Zygmund空间上的点乘子

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1041-1048.

• 论文 • 下一篇

单位球上正规权Zygmund空间上的点乘子

郭雨婷,尚清丽,张学军*()

湖南师范大学数学与统计学院长沙 410006

收稿日期:2017-09-12 出版日期:2018-12-26 发布日期:2018-12-27
通讯作者: 张学军 E-mail:xuejunttt@263.net
基金资助:
国家自然科学基金(11571104);湖南省重点学科建设项目

The Pointwise Multiplier on the Normal Weight Zygmund Space in the Unit Ball

Yuting Guo,Qingli Shang,Xuejun Zhang*()

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

Received:2017-09-12 Online:2018-12-26 Published:2018-12-27
Contact: Xuejun Zhang E-mail:xuejunttt@263.net
Supported by:
Supported by the NSFC(11571104);the Construct Program of the Key Discipline in Hunan Province

摘要/Abstract

摘要：

设μ是[0，1）上的一个正规函数，该文刻划了Cⁿ中单位球B上正规权Zygmund空间Z_μ（B）上的点乘子.给出了Z_μ（B）上乘子算子为有界算子或紧算子的充要条件.

关键词: 正规权Zygmund空间, 点乘子, 有界性, 紧性, 单位球

Abstract:

Let μ be a normal function on[0, 1). In this paper, the authors character the pointwise multipliers on the normal weight Zygmund space Z_μ(B) in the unit ball of Cⁿ. The necessary and sufficient conditions for the multiplier operator is bounded or compact are given.

Key words: Normal weight Zygmund space, Pointwise multiplier, Boundedness, Compactness, Unit ball

中图分类号:

O174.56

郭雨婷,尚清丽,张学军. 单位球上正规权Zygmund空间上的点乘子[J]. 数学物理学报, 2018, 38(6): 1041-1048.

Yuting Guo,Qingli Shang,Xuejun Zhang. The Pointwise Multiplier on the Normal Weight Zygmund Space in the Unit Ball[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1041-1048.

参考文献 25

1	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
2	韩秀, 徐辉明. Besov空间和Zygmund空间之间的复合算子. 数学研究, 2009, 42: 310- 319 doi: 10.3969/j.issn.1006-6837.2009.03.012
	Han X , Xu H M . Composition operators between Besov spaces and Zygmund spaces. J Math Study, 2009, 42: 310- 319 doi: 10.3969/j.issn.1006-6837.2009.03.012
3	Li S X , Stević S . Products of Volterra type operator and composition operator from H^∞ and Bloch spaces to Zygmund spaces. J Math Anal Appl, 2008, 345: 40- 52 doi: 10.1016/j.jmaa.2008.03.063
4	Stević S . On an integral operator from the Zygmund space to the Bloch type space on the unit ball. Glasgow Math J, 2009, 51: 275- 287 doi: 10.1017/S0017089508004692
5	Fang Z S , Zhou Z H . Extended Cesáro operators from generally weighted Bloch spaces to Zygmund space. J Math Anal Appl, 2009, 359: 499- 507 doi: 10.1016/j.jmaa.2009.06.013
6	Zhu X . A new characterization of the generalized weighted composition operator from H^∞ into the Zygmund space. Math Ineq Appl, 2015, 18: 1135- 1142
7	Wingren P . Characterization of the Zygmund space by Shifted B-Splines. J Appro Theory, 2001, 111: 256- 266 doi: 10.1006/jath.2001.3575
8	Li S X , Stević S . Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces. Appl Math Comput, 2010, 217: 3144- 3154
9	Liu Y M , Yu Y Y . Weighted differentiation composition operators from mixed-norm to Zygmund spaces. Numer Funct Anal Opt, 2010, 31: 936- 954 doi: 10.1080/00268976.2010.505108
10	Li S X , Stević S . On an integral-type operator from ω-Bloch spaces to μ-Zygmund spaces. Applied Math Comput, 2010, 215: 4385- 4391
11	Zhang X J , Li M , Guan Y . The equivalent norms and the Gleason's problem on μ-Zygmund spaces in Cⁿ. J Math Anal Appl, 2014, 419: 185- 199 doi: 10.1016/j.jmaa.2014.04.058
12	Stević S. On an integral-type operator from Zygmund-type spaces to mixed-norm spaces on the unit ball. Abstr Appl Anal, 2010, Article ID: 198608
13	Taylor G D . Multipliers on D_α. Trans Amer Math Soc, 1966, 123: 229- 240
14	Stegenga D A . Multipliers of the Dirichlet space. Illinois J Math, 1980, 24: 113- 139
15	Hu P Y , Shi J H . Multipliers on Dirichlet type spaces. Acta Math Sin, 2001, 17: 263- 272 doi: 10.1007/s101149900008
16	Zhu K H . Multipliers of BMO in the Bergman metric with applications to Toeplitz operators. J Funct Anal, 1989, 87: 31- 50 doi: 10.1016/0022-1236(89)90003-7
17	Zhang X J . The pointwise multipliers of Bloch type space β^p and Dirichlet type space D_q on the unit ball of Cⁿ. J Math Anal Appl, 2003, bf 285: 376- 386
18	Axler S , Shields A L . Univalent multipliers of the Dirichlet space. Michigan Math J, 1985, 32: 65- 80 doi: 10.1307/mmj/1029003133
19	张学军, 王敏. Cⁿ中单位球上p-Bloch上的点乘子. 数学研究, 2001, 34: 158- 163 doi: 10.3969/j.issn.1006-6837.2001.02.011
	Zhang X J , Wang M . The pointwise multipliers of p-Bloch space in the unit ball of Cⁿ. J Math Study, 2001, 34: 158- 163 doi: 10.3969/j.issn.1006-6837.2001.02.011
20	Hu Z J . Composition operators between Bloch-type spaces in the polydisc. Science in China Ser A, 2005, 48 (Supp): 1- 15
21	张学军, 李菊香. Cⁿ中单位球上μ-Bloch空间之间的复合算子. 数学物理学报, 2009, 29 (29A): 573- 583
	Zhang X J , Li J X . Weighted composition operators between μ-Bloch spaces on the unit ball of Cⁿ. Acta Math Sci, 2009, 29A: 573- 583
22	Zhang X J , Xiao J B . Weighted composition operators between μ-Bloch spaces on the unit ball. Science in China, 2005, 48A (10): 1349- 1368
23	Zhang X J , Xi L H , Fan H X , Li J F . Atomic decomposition of μ-Bergman space in Cⁿ. Acta Math Sci, 2014, 34B (3): 779- 789
24	Li S L , Zhang X J , Xu S . The compact composition operator on the μ-Bergman Space in the unit ball. Acta Math Sci, 2017, 37B (2): 425- 438
25	赵艳辉,张学军.单位球上Dirichlet型空间到Z_μ型空间的积分型算子.数学物理学报, 2017, 37A(2): 217-227
	Zhao Y H, Zhang X J. On an integral-type operator from Dirichlet spaces to Zygmund type spaces on the unit ball. Acta Math Sci, 37A(2): 217-227

Metrics

Viewed

Full text

258

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	11	0	0	247

From	Others	local

Times	13	245
Rate	5%	95%

Abstract

123

Just accepted	Online first	Issue

0	0	123

	From	Others

	Times	123
	Rate	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

[1]	黄子晏, 赵迪, 李红裔. 复空间Cⁿ中有界多重调和映射的Schwarz-Pick引理[J]. 数学物理学报, 2018, 38(3): 433-445.
[2]	王晚生, 钟鹏, 赵新阳. 非线性中立型变延迟微分方程的长时间稳定性[J]. 数学物理学报, 2018, 38(1): 96-109.
[3]	赵磊娜. 退化拟线性椭圆方程的均匀化[J]. 数学物理学报, 2017, 37(5): 860-868.
[4]	高红亚, 贾苗苗. 障碍问题解的局部正则性和局部有界性[J]. 数学物理学报, 2017, 37(4): 706-713.
[5]	赵阳, 彭茹. Cⁿ单位球中F(p,q,s)空间上的原子分解[J]. 数学物理学报, 2017, 37(3): 416-426.
[6]	赵艳辉, 张学军. 单位球上Dirichlet型空间到Z_μ型空间的积分型算子[J]. 数学物理学报, 2017, 37(2): 217-227.
[7]	杜广伟, 钮鹏程. 非线性次椭圆方程障碍问题很弱解的高阶可积性[J]. 数学物理学报, 2017, 37(1): 122-145.
[8]	郜欣春, 周健, 田苗青. 带有Logistic源的吸引-排斥趋化性系统的整体有界性和渐近行为[J]. 数学物理学报, 2017, 37(1): 113-121.
[9]	王胜华, 吴红星. Rotenberg模型中一类迁移算子的谱分析[J]. 数学物理学报, 2016, 36(5): 821-831.
[10]	夏治南. Volterra-Stieltjes型泛函积分方程解的存在性及渐近行为[J]. 数学物理学报, 2016, 36(1): 130-143.
[11]	夏锦, 王晓峰, 曹广福. 调和Dirichlet空间D_h¹上有界、紧与Fredholm的Toeplitz算子[J]. 数学物理学报, 2015, 35(5): 956-969.
[12]	陆恒, 张太忠. 从α-Zygmund空间到β-Bloch空间的加权复合算子[J]. 数学物理学报, 2015, 35(4): 748-755.
[13]	谭春雨, 王茂发. 从Zygmund空间和F(p,q,s)空间到B^μ空间的广义复合算子[J]. 数学物理学报, 2015, 35(4): 815-823.
[14]	谢胜利. 有阻尼的二阶脉冲无穷时滞泛函微分方程解的存在性[J]. 数学物理学报, 2015, 35(1): 97-109.
[15]	刘竟成, 李俊锋, 张学军. Cⁿ中单位球上Dirichlet型空间的Cesaro 算子[J]. 数学物理学报, 2015, 35(1): 182-193.

单位球上正规权Zygmund空间上的点乘子

The Pointwise Multiplier on the Normal Weight Zygmund Space in the Unit Ball

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献 25

相关文章 15

Metrics

本文评价

推荐阅读 10