摘要
首先定义了复平面C上加权可积函数空间L^(p)-空间L_(α)^(P)(C,dA)、调和Fock空间F_(h,α)^(2)上以本性有界函数φ为符号的乘法算子M_(φ)与Toeplitz算子T_φ。接着研究了L_(α)^(P)(C,dA)空间上乘法算子M_(φ)的基本性质,包括其共轭算子的表示,M_(φ)是L_(α)^(P)(C,dA)空间上有界线性算子的充分必要条件是φ为复平面C上的有界函数;M_(φ)是自伴算子当且仅当φ为复平面C上的实值函数;M_(φ)在L_(α)^(P)(C,dA)是可逆算子当且仅当φ可逆以及M_(φ)谱。最后讨论了调和Fock空间F_(h,α)^(2)上Toeplitz算子T_(φ)基本性质,包括其线性、共轭算子的表示;并且得到T_(φ)在F_(h,α)^(2)上为有界线性算子的一个充分条件是:φ为复平面C上的有界函数。
Firstly,multiplication operators M_(φ)on weighted integrable function space Lp-spaces L_(α)^(P)(C,dA)and Toeplitz operators T_(φ)on harmonic Fock spaces F_(h)^(2),αwith the essential bounded functionsφas symbol on the complex plane C are defined.Next,the basic properties of multiplication operators M_(φ)on spaces L_(α)^(P)(C,dA)including the representation of the conjugate operator of M_(φ)are studied,obtaining the necessary and sufficient condition of boundedness for M_(φ)on spaces L_(α)^(P)(C,dA)is that φ is a bounded function on the complex plane C;M_(φ)is a self-adjoint operator if and only if φ is a real function on the complex plane C;and M_(φ)is invertible on spaces L_(α)^(P)(C,dA)if and only if φ is a invertible function and spectrum of M_(φ).Lastly,the basic properties of Toeplitz operators T_(φ)on harmonic Fock spaces F_(h)^(2),α including the linearity and conjugate operator are discussed,obtaining a sufficient condition for boundedness of T_(φ)on harmonic Fock spaces F_(h,α)^(2) is thatφis a bounded function on the complex plane C.
作者
李勇强
黃穗
LI Yongqiang;HUANG Sui(School of Mathematical Science,Chongqing Normal University,Chongqing 401331,China)
出处
《四川轻化工大学学报(自然科学版)》
2025年第4期124-128,共5页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金
国家自然科学基金项目(11871127)
重庆市科委科研项目(CSTC2019JCYJ-MSXM0295)
重庆师范大学数学科学学院重点实验室开放课题项目(CSSXKFKTM202002)。
