Growth, zero distribution and factorization of analytic functions of moderate growth in the unit disc

Abstract

We give a survey of results on zero distribution and factorization of analytic functions in the unit disc in classes defined by the growth of $\log|f(re^{i\theta})|$ in the uniform and integral metrics. We restrict ourself by the case of finite order of growth. For a Blaschke product $B$ we obtain a necessary and sufficient condition for the uniform boundedness of all $p$-means of $\log|B(re^{i\theta})|$, where $p>1$.