Growth of pth means of analytic and subharmonic functions in the unit disc and angular distribution of zeros

2015/09/07 by Igor Chyzhykov, Chyzhykov, Igor
Mathematics · #30H05 #30J10 #31A05 #31A10 #31A20 #31A25 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1509.02141

openalex publication_date 2015/09/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Answering a question of A.Zygmund in \citeMR G.MacLane and L.Rubel described boundedness of L₂-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 pth means, p∈(1, ∞), 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 pth means of analytic and subharmonic functions of finite order in the unit disc.

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