Stochastic convolutions driven by a local martingale M in a Hilbert space are studied in the case when S(t) is a strongly continuous semigroup of contractions. Very simple proofs of the maximal inequality and exponential tail estimates are given by using unitary dilations and Zygmund's extrapolation theorem. Applications to stochastic convolutions driven by Poisson random measures are provided. A part of the results is then generalized to stochastic convolutions in L^q-spaces.