Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet

We obtain some new estimates for the small ball behavior of the d-dimensional fractional Brownian sheet under Holder and Orlicz norms. For d=2, these bounds are sharp for the Orlicz and the sup-norm. In addition, we give bounds for the Kolmogorov and entropy numbers of some operators satisfying an L 2-Holder-type condition.