We generalize the Riesz conjugate functions theorem for planar harmonic K-quasiregular mappings (when 1<p≤2) and harmonic K-quasiconformal mappings (when 2<p<∞) in the unit disk. Moreover, if K=1, then our constant coincides with the classical analytic case. For the n dimensional case (n>2), we also obtain the Riesz conjugate functions theorem for invariant harmonic K-quasiregular mappings when 1<p≤2. 

Publication: 

Advances in Mathematics, Volume 434, 1 December 2023, 109321 

http://dx.doi.org/10.1016/j.aim.2023.109321 

Author: 

Jinsong Liu 

HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China 

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 

Email: liujsong@math.ac.cn 

Jian-Feng Zhu 

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China