Two criteria for $P_h$-sequences

The notion of $P_h$-sequence was introduced by V. I. Gavrilov as a natural generalization of $P$-sequences (Math. Rev., v. 36, 385). We prove two criteria for a sequence of points in $D\colon|z|<1$ to be a $P_h$-sequence of a given meromorphic function defined in $D$. The first of them generalizes a known criterion for $P$-sequences formulated in terms of spherical derivative.