Hölder estimates for the noncommutative Mazur maps

For any von Neumann algebra MM, the noncommutative Mazur map Mp,qMp,q from Lp(M)Lp(M) to Lq(M)Lq(M) with 1p,q<1≤p,q<∞ is defined by ff|f|pqqf↦f|f|p-qq. In analogy with the commutative case, we gather estimates showing that Mp,q is min{pq,1}min{pq,1}-Hölder on balls.