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arXiv · 2312.06894

Schwarz-Pick Lemma for $(\alpha, \beta)$-Harmonic Functions in the Unit Disc

Miloš Arsenović·Jelena Gajić
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Abstract

We obtain Schwarz-Pick lemma for $(\alpha, \beta)$-harmonic functions u in the disc, where $\alpha$ and $\beta$ are complex parameters satisfying $\Re \alpha + \Re \beta > -1$. 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 $\alpha$-harmonic and $T_\alpha$-harmonic functions.

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Miloš Arsenović, Jelena Gajić. 2023-12-11. Schwarz-Pick Lemma for $(\alpha, \beta)$-Harmonic Functions in the Unit Disc. https://arxiv.org/abs/2312.06894

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