A generalization of a result of Choa on analytic functions with Hadamard gaps

In this paper we obtain a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for f (z)=E-k=1(infinity) P-n k(z) (the homogeneous polynomial expansion of f) satisfying n(k+1)/n(k)>=lambda>1 for all k is an element of N, to belong to the weighted Bergman space A(alpha)(p)(B) = {f vertical bar integral(B)vertical bar f(z)vertical bar(p)(1-vertical bar z vertical bar(2))(alpha)dV(z)<infinity, f is an element of H(B)}. We find a growth estimate for the integral mean (integral(partial derivative B)vertical bar f(r zeta)vertical bar(p)d sigma(zeta))(1/p), and an estimate for the point evaluations in this class of functions. Similar results on the mixed norm space H-p,H-q,H-alpha(B) and weighted Bergman space on polydisc A(<(alpha)over bar>)(p)(U-n) are also given.