Schwarz-Pick Lemma for $(α, β)$-Harmonic Functions in the Unit Disc
We obtain Schwarz-Pick lemma for $(α, β)$-harmonic functions u in the disc, where $α$ and $β$ are complex parameters satisfying $\Re α+ \Re β> -1$. We prove sharp estimate of derivative at the origin for such functions in terms of $L^p$ norm of the boundary function. Also, we give asymptotically sharp estimate of the norm of the derivative at point $z$ in the unit disc. These estimates are extended to higher order derivatives. Our results extend earlier results for $α$-harmonic and $T_α$-harmonic functions.
math.CV↗