胡馨, 黄穗. Fock空间F_α^p上的Toeplitz算子J. 内江师范学院学报, 2026, 41(10): 18-22. DOI: 10.13603/j.cnki.51-1621/z.2026.10.003
    引用本文: 胡馨, 黄穗. Fock空间F_α^p上的Toeplitz算子J. 内江师范学院学报, 2026, 41(10): 18-22. DOI: 10.13603/j.cnki.51-1621/z.2026.10.003
    HU Xin, HUANG Sui. Toeplitz operators on the Fock spaces F_α^pJ. Journal of Neijiang Normal University, 2026, 41(10): 18-22. DOI: 10.13603/j.cnki.51-1621/z.2026.10.003
    Citation: HU Xin, HUANG Sui. Toeplitz operators on the Fock spaces F_α^pJ. Journal of Neijiang Normal University, 2026, 41(10): 18-22. DOI: 10.13603/j.cnki.51-1621/z.2026.10.003

    Fock空间F_α^p上的Toeplitz算子

    Toeplitz operators on the Fock spaces F_α^p

    • 摘要: 受Isralowitz关于Fock空间上弱局部算子性质讨论的启发, 以算子的Berezin变换为工具, 研究Fock空间F_α^p(1<p<+∞)上以BMO中函数φ为符号的Toeplitz算子Tφ的有界性和紧性.将Tφ在F_α^2上的性质推广到F_α^p上,得到两个主要结果:Tφ是Fock空间F_α^p上的有界算子当且仅当φ的Berezin变换\widetilde\varphi有界,Tφ是Fock空间F_α^p上的紧算子当且仅当\widetilde\varphi∈C0(\mathbbC).如果φ是BMO中的调和函数, 那么Tφ在F_α^p上有界当且仅当φ有界, Tφ在F_α^p上紧当且仅当φ∈C0(\mathbbC).

       

      Abstract: In this paper, enlightened by Isralowitz’s works on the properties of weakly localized operators on Fock spaces, we use Berezin transform as a key tool to investigate boundedness and compactness of Toeplitz operators Tφ with symbols φ in BMO on the Fock spaces F_α^p(1<p<+∞). We extend properties of Tφ on F_α^2 to the more general F_α^p setting, yielding two main results: Tφ is a bounded operator on F_α^p if and only if the Berezin transform \widetilde\varphi of φ is bounded, Tφ is a compact operator on F_α^p if and only if \widetilde\varphi∈C0(\mathbbC). If φ is harmonic function of BMO, then Tφ is bounded on F_α^p if and only if φ is bounded, Tφ is compact on if and only if φ∈C0(\mathbbC).

       

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