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1. Commuting Toeplitz Operators with Harmonic Symbols on A^2(overline{mathbb{D}},dmu)$ | |||
Ji You Qing,Wang Chunmei | |||
Mathematics 06 January 2009 | |||
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Abstract:For any given symmetric measure u on the closed unit disk $overline{mathbb{D}}$, by characterizingthe relationship between the Berezin transform and harmonic functions, we obtain that if both $f$ and $g$ are bounded harmonic on $mathbb{D}$, then the Toeplitz operator $T_f$ commutes with $T_g$ on $A^2(overline{mathbb{D}},dmu)$ if and only if at least one of the following conditions holds: (1) both $f$ and $g$ are analytic on $mathbb{D}$; (2) both $overline{f}$ and $overline{g}$ are analytic on $mathbb{D}$;(3) there exist constants $a,binmathbb{C}$, not both 0, such that $af+bg$ is constant on $mathbb{D}$. | |||
TO cite this article:Ji You Qing,Wang Chunmei. Commuting Toeplitz Operators with Harmonic Symbols on A^2(overline{mathbb{D}},dmu)$ [OL].[ 6 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27386 |
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