On the regularity of the growth of the modulus and argument of an entire function in the metric of L^p [0, 2π] - Kalinets, R. Z.; Koval’chuk, Yu. A. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
Under sufficiently general assumptions, we describe sets of entire functions f, sets of growing functions λ, and sets of complex-valued functions H from L^p [0, 2π], p ∈ [1, + ∞], for which { 12π _0^2π |f(re^iθ ) - λ (r)H(θ )|^p dθ }^1/p = o(λ (r)),r → ∞.