Coefficients and Integral Mean Estimates for K-Quasiconformal Harmonic Mappings
Abstract
Recently, Li and Ponnusamy~\cite{LiPonnusamy2025} established the coefficient conjecture proposed by Wang et al.~\cite{Wang2024} for several prominent geometric subclasses of 𝒮0H(K), the class of sense-preserving K-quasiconformal univalent harmonic mappings in the unit disk. In this paper, we show that the conjecture continues to hold for a class of K-quasiconformal harmonic mappings defined via quasi-subordination. Further, we determine the range of p>0 for which such mappings belong to the Hardy space bf hp and the weighted Bergman space apβ, for β>−1. Our Hardy space result makes significant progress toward a problem posed by Pavlović, while the Bergman space result sharpens the range obtained by Das and Rasila~\cite{DasRasila}, doubling the previously known bounds. In addition, we obtain refined growth and integral mean estimates for the subclass, improving earlier results and providing further evidence toward an open problem raised by Das et al.~\cite{DasRasila2025}. Parallel results are also discussed for odd K-quasiconformal harmonic mappings.
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BibTeX
@misc{parashar2026coefficients,
title = {{Coefficients and Integral Mean Estimates for $K$-Quasiconformal Harmonic Mappings}},
author = {Jasbir Parashar and Saminathan Ponnusamy and A. Sairam Kaliraj},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28121},
eprint = {2608.28121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28121},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Coefficients and Integral Mean Estimates for K-Quasiconformal Harmonic Mappings
AU - Jasbir Parashar
AU - Saminathan Ponnusamy
AU - A. Sairam Kaliraj
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28121
UR - https://arxiv.org/abs/2608.28121
AB - Recently, Li and Ponnusamy~\cite{LiPonnusamy2025} established the coefficient conjecture proposed by Wang et al.~\cite{Wang2024} for several prominent geometric subclasses of 𝒮^0_H(K), the class of sense-preserving K-quasiconformal univalent harmonic mappings in the unit disk. In this paper, we show that the conjecture continues to hold for a class of K-quasiconformal harmonic mappings defined via quasi-subordination. Further, we determine the range of p>0 for which such mappings belong to the Hardy space bf h^p and the weighted Bergman space a^p_β, for β>−1. Our Hardy space result makes significant progress toward a problem posed by Pavlović, while the Bergman space result sharpens the range obtained by Das and Rasila~\cite{DasRasila}, doubling the previously known bounds. In addition, we obtain refined growth and integral mean estimates for the subclass, improving earlier results and providing further evidence toward an open problem raised by Das et al.~\cite{DasRasila2025}. Parallel results are also discussed for odd K-quasiconformal harmonic mappings.
ER -