Growth properties and sequences of zeros of analytic functions in spaces of Dirichlet type

For 0 < p < infinity, we let D-p-1(p), denote the space of those functions f that are analytic in the unit disc Delta = {z is an element of C : vertical bar z vertical bar < 1} and satisfy integral(Delta)(1 - vertical bar z vertical bar)(p-1)vertical bar f'(z)vertical bar(p) dx dy < infinity. The spaces D-p-1(p) are closely related to Hardy spaces. We have, D-p-1(p) C H-p, if 0 < p <= 2, and H-p subset of D-p-1(p), if 2 <= p < infinity. In this paper we obtain a number of results about the Taylor coefficients of D-p-1(p)-funuions and sharp estimates on the growth of the integral means and the radial growth of these functions as well as information on their zero sets.