On sum of values of functions from certain classes on sequence of points (Q1311160)

The author studies the following problem. Let \(D = \{x \in \mathbb{R}^ m: | x| < 1\}\), \(m \geq 2\); let \(\mathcal F\) be a class of \(\delta\)- subharmonic functions in \(D\); and let \(\Phi(t)\) be an increasing function on \((-\infty,\infty)\), positive and such that \(\Phi(t) \to 0\) as \(t\to - \infty\). What conditions on a sequence \(x_ n \in D\), \(| x_ n| \to 1\), guarantee that for each \(u \in {\mathcal F}\) one has \(\sum_ n \Phi(u(x_ n)) = +\infty ?\) A number of such conditions are given with applications to meromorphic functions of bounded characteristics in the unit disk.