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Some Properties of Mappings Admitting General Poisson Representations

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Abstract

The aim of this paper is twofold. First, we adapt the Burgeth’s spherical cap method [Manuscripta Math. 77:283–291, 1992 by Burgeth and Proceedings of the NATO Advanced Research Workshop on Classical and Modem Potential Theory and Applications, pp 133–147, 1994 by Burgeth] to the planar case to establish some Schwarz type lemmas for mappings admitting general Poisson type representations on the unit disk. Second, we prove a Landau type theorem for \(T_\alpha \)-harmonic functions introduced by Olofsson (J Anal Math 123:227–249, 2014).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Adel Khalfallah

  2. Faculty of mathematics, University of Belgrade, Studentski Trg 16, Belgrade, Republic of Serbia

    Miodrag Mateljević

  3. Ecole superieure des Sciences et de la Technologie de Hammam Sousse (ESSTHS), Université de Sousse, Sousse, Tunisia

    Mohamed Mhamdi

Authors
  1. Adel Khalfallah
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  2. Miodrag Mateljević
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  3. Mohamed Mhamdi
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Correspondence to Adel Khalfallah.

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Khalfallah, A., Mateljević, M. & Mhamdi, M. Some Properties of Mappings Admitting General Poisson Representations. Mediterr. J. Math. 18, 193 (2021). https://doi.org/10.1007/s00009-021-01827-0

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  • DOI: https://doi.org/10.1007/s00009-021-01827-0

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