Abstract
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.
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