Growth of $p$th means of analytic and subharmonic functions in the unit disc and angular distribution of zeros

Abstract

Answering a question of A.Zygmund in \cite{MR} G.MacLane and L.Rubel described boundedness of $L_2$-norm w.r.t. the argument of $\log |B|$, where $B$ is a Blaschke product. We generalize their results in several directions. We describe growth of $p$th means, $p\in (1,\infty )$, of subharmonic functions bounded from above in the unit disc. Necessary and sufficient conditions are formulated in terms of the complete measure (of a subharmonic function) in the sense of A.Grishin. We also prove sharp estimates of the growth of $p$th means of analytic and subharmonic functions of finite order in the unit disc.

19 pages

Cited by in corpus (1)

• Growth description of $p$th means of the Green potential in the unit ball