For , we prove sharp weak-type -estimates for the Beurling–Ahlfors operator acting on the radial function subspaces of . A similar sharp -result is proved for . The results are derived from martingale inequalities which are of independent interest.
"Sharp inequalities for the Beurling–Ahlfors transform on radial functions." Duke Math. J. 162 (2) 417 - 434, 1 February 2013. https://doi.org/10.1215/00127094-1962649