Sharp Pointwise Estimates for Fock Spaces

Let 1 ≤ p < ∞ , and α > 0 . Let F α p denote the Fock space. We establish some sharp pointwise estimates for the derivatives of the functions belonging to F α p . Moreover for the Hilbert case p = 2 we establish some more specific pointwise sharp estimates. We also consider the differential operator between F α p and F β p for β > α and its adjoint.