Schwarz-Pick lemma for (α,β)-harmonic functions in the unit disc

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 ℜα+ℜβ>−1. We prove sharp estimate of ‖Du(0)‖ for such functions in terms of Lp norm of the boundary function. Also, we give asymptotically sharp estimate of ‖Du(z)‖. This estim...

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Veröffentlicht in:Journal of mathematical analysis and applications 2024-11, Vol.539 (1), p.128489, Article 128489
Hauptverfasser: Arsenović, Miloš, Gajić, Jelena
Format: Artikel
Sprache:eng
Schlagworte:
[formula omitted]-harmonic functions
Poisson integral
Schwarz lemma
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Zusammenfassung:We obtain Schwarz–Pick lemma for (α,β)-harmonic functions u in the disc, where α and β are complex parameters satisfying ℜα+ℜβ>−1. We prove sharp estimate of ‖Du(0)‖ for such functions in terms of Lp norm of the boundary function. Also, we give asymptotically sharp estimate of ‖Du(z)‖. This estimate is generalized to higher order derivatives. Our results extend earlier results for α-harmonic and Tα-harmonic functions.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128489