Toeplitz Operators from One Fock Space to Another |
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Authors: | Zhangjian Hu Xiaofen Lv |
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Institution: | 1.Huzhou Teachers College,Huzhou,People’s Republic of China |
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Abstract: | In this paper, we study Toeplitz operators T μ from one Fock space \({F^{p}_{\alpha}}\) to another \({F^{q}_{\alpha}}\) for 1 < p, q < ∞ with positive Borel measures μ as symbols. We characterize the boundedness (and compactness) of \({T_\mu: F^{p}_{\alpha} \to F^{q}_{\alpha}}\) in terms of the averaging function \({\widehat{\mu}_r}\) and the t-Berezin transform \({\widetilde{\mu}_t}\) respectively. Quite differently from the Bergman space case, we show that T μ is bounded (or compact) from \({F^{p}_{\alpha}}\) to \({F^{q}_{\alpha}}\) for some p ≤ q if and only if T μ is bounded (or compact) from \({F^{p}_{\alpha}}\) to \({F^{q}_{\alpha}}\) for all p ≤ q. In order to prove our main results on T μ , we introduce and characterize (vanishing) (p, q)-Fock Carleson measures on C n . |
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