Let \(1\le p<\infty \), and \(\alpha >0\). Let \(F_{\alpha }^{p}\) denote the Fock space. We establish some sharp pointwise estimates for the derivatives of the functions belonging to \(F_{\alpha }^{p}\). Moreover for the Hilbert case \(p=2\) we establish some more specific pointwise sharp estimates. We also consider the differential operator between \(F_{\alpha }^{p}\) and \(F_{\beta }^{p}\) for \(\beta >\alpha \) and its adjoint.

中文翻译：

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Fock空间的敏锐逐点估计

令\（1 \ le p <\ infty \）和\（\ alpha> 0 \）。令\（F _ {\ alpha} ^ {p} \）表示Fock空间。我们为属于\（F _ {\ alpha} ^ {p} \）的函数的导数建立一些尖锐的逐点估计。此外，对于希尔伯特案例\（p = 2 \），我们建立了一些更具体的逐点尖锐估计。我们还考虑之间的微分算子\（F _ {\阿尔法} ^ {P} \）和\（F _ {\的β} ^ {P} \）为\（\的β> \阿尔法\）和它的伴随。