Toeplitz and Hankel operators with L∞,1 symbols on Dirichlet space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Chen, Yong^1,2  Nguyen Quang Dieu^3,4 

[1] Zhejiang Normal Univ, Coll Math Phys & Informat Engn, Jinhua 321004, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Hanoi Univ Educ Dai Hoc Pham Hanoi, Dept Math, Hanoi, Vietnam

[4] Chonnam Natl Univ, Dept Math, Kwangju 700757, South Korea

关键词: Toeplitz operator;    Hankel operator;    Sobolev space;    Dirichlet space;    Commutativity;    Fredholm property;   

DOI  :  10.1016/j.jmaa.2010.03.025

来源: Elsevier

【 摘 要 】

We show that Toeplitz or small Hankel operators with symbols in L-infinity,L-1 is a generalization of the case with the harmonic symbol in C circle plus D circle plus (D) over bar, where D is the Dirichlet space on D. We also give a decomposition theorem for the Sobolev space of first order on D. Using this result, some characterizations for algebraic properties of Toeplitz or small Hankel operators with symbols in L-infinity,L-1 are given. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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