General páley problem

Abstract

In the class of functions u of finite lower order subharmonic in ℝ ^p+2,p ∈ ℕ we establish an exact upper bound for $$\mathop {\lim }\limits_{r \to \infty } \inf \frac{{m_q (r,u^ + )}}{{T(r,u)}}, 1< q \le \infty ,$$ whereT(r, u) is a Nevanlinna characteristic of the function u andm _q (r, u ⁺) is the integralq-mean of the functionu ⁺,u ⁺ = max(u,0), on the sphere of radiusr