| Citation: |
LI Dongxing, ZHUO Zhengyuan, ZENG Tiaoying. The Multiplier Algebra of Dirichlet Space[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(5): 88-92. DOI: 10.6054/j.jscnun.2023067
|
In order to enrich the theory of the Dirichlet space, the mathematical structure of the multiplier algebra of Dirichlet space is studied by applying concepts of inner function and outer function. At first, the inclusion relations between multiplier algebra, intersection set algebra and Dα algebra of Dirichlet space is given and then properties of their inner function and outer function is investigated. Finally, the quotient decomposition theory of outer function in multiplier algebra of Dirichlet space was obtained.
| [1] |
ADAM R. Sobolev spaces[M]. New York: Academic Press, 1975.
|
| [2] |
STEGENGA A. Multipliers of the Dirichlet space[J]. Illinois Journal of Mathematics, 1980, 24: 113-139.
|
| [3] |
WU Z J. Carleson measures and multipliers for Dirichlet spaces[J]. Journal of Functional Analysis, 1999, 169: 148-163. doi: 10.1006/jfan.1999.3490
|
| [4] |
BAO G L, LOU Z J, QIAN R S. On multipliers of Dirichlet type spaces[J]. Complex Analysis and Operator Theory, 2015, 9: 1701-1732. doi: 10.1007/s11785-015-0444-0
|
| [5] |
AULASKARI R, WULAN H S. Outer functions in Qp#[J]. Journal of Function Spaces and Applications, 2004, 2: 17-24. doi: 10.1155/2004/493269
|
| [6] |
WULAN H S. Quotient decomposition of Qp# functions[J]. Annales Academiae Scientiarum Fennicae Mathematica, 2004, 29: 283-293.
|
| [7] |
李东行, 乌兰哈斯. QK乘子代数上的Corona定理和Wolff定理[J]. 中国科学: 数学A辑, 2021, 51(2): 301-314. LI D X, WULAN H S. Corona and Wolff theorems for the multiplier algebras of QK space[J]. Science in China: Series A, 2021, 51(2): 301-314.
|
| [8] |
LI D X, WULAN H S, ZHAO R H. DK spaces and Carleson measures[J]. Acta Mathematica Scientia, 2022, 42(3): 1-10.
|
| [9] |
EL-FALLAH O, KELLAY K, MASHREGHI J, et al. A pri-mer on the Dirichlet space[M]. New York: Cambridge University Press, 2014.
|
| [10] |
EL-FALLAH O, ELMADANI Y, KELLAY K. Kernel and capacity estimates in Dirichlet spaces[J]. Journal of Functional Analysis, 2019, 276(3): 867-895.
|
| [11] |
DOUGLAS R. Banach algebra techniques in operator theory[M]. New York: Academic Press, 1972.
|
| [12] |
GARNETT J. Bounded analytic functions[M]. New York: Academic Press, 1981.
|
| [13] |
ZHU K. Operator theory on function spaces[M]. New York: Marcel Dekker, 2007.
|
| [14] |
夏道行, 吴卓人, 严绍宗, 等. 实变函数与泛函分析[M]. 北京: 高等教育出版社, 2010.
|
| [15] |
DUREN P. Theory of Hp spaces[M]. New York: Academic Press, 1970.
|
| [16] |
MASHREGHI G S, ROSS J. Finite Blaschke products and their connections[M]. Switzerland: Springer, 2018.
|
| [17] |
ALEMAN A. A conjecture of L. Carleson and applications[J]. Michigan Mathematical Journal, 1992, 39: 537-549.
|
| 1. |
王文庆，孙柯，黄世奇，卢莹. 改进的暗通道先验图像去雾霾算法. 西安邮电大学学报. 2023(02): 65-71 .
| |
| 2. |
杜渺勇，于祥雨，周浩，韩丹夫. 基于自编码卷积神经网络的图像去噪算法. 杭州师范大学学报(自然科学版). 2021(01): 95-101 .
| |
| 3. |
李树平，张辽，刘俊利. 基于天空区域分割和条件约束优化的图像去雾研究. 河南理工大学学报(自然科学版). 2021(05): 132-138 .
| |
| 4. |
杨昊岩，栾涛，韩仲志，倪建功，高霁月. 基于深度学习声谱图分类的“听声识风”. 华南师范大学学报(自然科学版). 2021(05): 10-16 .
|
Supported by: Beijing Renhe Information Technology Co., Ltd. 
DownLoad: