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

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.