February 25, 2024Open Access

Sharp pointwise estimate of -harmonic functions

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Abstract

Let >-1 and assume that f is -harmonic mapping defined in the unit disk that belongs to the Hardy class hᵖ with p 1. We obtain some sharp estimates of the type |f (z) | g (|r|) \|f^\|ₚ and |Df (z) | h (|r|) \|f^\|ₚ. We also prove a Schwarz type lemma for the class of -harmonic mappings of the unit disk onto itself fixing the origin.

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David Kalaj (Sun,) studied this question.

synapsesocial.com/papers/68e77b35b6db6435876ef958 https://doi.org/https://doi.org/10.48550/arxiv.2402.16062

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