Schwarz–Pick Lemma for Harmonic and Generalized Harmonic Functions

We give an overview of results relating to derivative estimates and distance estimates for $$(\alpha,\beta)$$ -harmonic functions and for certain, depending on two parameters, classes of functions admitting a Poisson-type integral representation. Historical development is presented, which includes discussion of various special cases which appeared in the literature. In particular, the standard harmonic case is considered. Connections with other lines of research are pointed out.