Hadamard product in Qp spaces

We consider some theorems of the form f is an element of X, g is an element of Y double right arrow f * g is an element of Z, for various classes of analytic functions. For example, we can take X = Q(p), Y = Bloch space, and Z = Q(p), 0 < p < 1, which improves a result of Aulaskari, Girela and Wulan [Taylor coefficients and mean growth of the derivative of Qp functions, J. Math. Anal. Appl. 258 (2001) 415-428 (Theorem 2. 1)]. Also, we briefly discuss applications to lacunary series and random series. (c) 2004 Elsevier Inc. All rights reserved.