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 $f(z);=;{sum}^{infty}_{k=1};P_{nk}(z)$ (the homogeneous polynomial expansion of f) satisfying $n_{k+1}/n_{k}{ge}{lambda}>1$ for all $k;{in};N$, to belong to the weighted Bergman space $$A^p_{alpha}(B);=;{f{mid}{int}_{B}{mid}f(z){mid}^{p}(1-{mid}z{mid}^2)^{alpha}dV(z) < {infty},;f{in}H(B)}$$. We find a growth estimate for the integral mean $$({int}_{{partial}B}{mid}f(r{zeta}){mid}^pd{sigma}({zeta}))^{1/p}$$, and an estimate for the point evaluations in this class of functions. Similar results on the mixed norm space $H_{p,q,{alpha}$(B) and weighted Bergman space on polydisc $A^p_{^{ o}_{alpha}}(U^n)$ are also given.