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arXiv · 2509.17578

Conjugate type properties of harmonic $(K,K')$-quasiregular mappings

Shaolin Chen·David Kalaj
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Abstract

The main purpose of this paper is to investigate conjugate type properties for harmonic $(K,K')$-quasiregular mappings, where $K \geq 1$ and $K' \geq 0$ are constants. We first establish a Riesz type conjugate function theorem for such mappings, which generalizes and refines several existing results. Additionally, we derive an asymptotically sharp constant for a Riesz type theorem pertaining to a specific class of $K$-quasiregular mappings. Furthermore, we obtain Kolmogorov type and Zygmund type theorems for harmonic $(K,K')$-quasiregular mappings.

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Shaolin Chen, David Kalaj. 2025-09-22. Conjugate type properties of harmonic $(K,K')$-quasiregular mappings. https://arxiv.org/abs/2509.17578

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