For harmonic K-quasiregular mappings in the unit disk, the real and imaginary parts have the same order of integral-mean growth for all p>0, and share alpha-Hölder boundary smoothness for 0<alpha<1.
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Note on real and imaginary parts of harmonic quasiregular mappings
For harmonic K-quasiregular mappings in the unit disk, the real and imaginary parts have the same order of integral-mean growth for all p>0, and share alpha-Hölder boundary smoothness for 0<alpha<1.