Abstract
For any von Neumann algebra \({\mathcal{M}}\), the noncommutative Mazur map \({M_{p,q}}\) from \({L_p(\mathcal{M})}\) to \({L_q(\mathcal{M})}\) with \({1\leq p, q < \infty}\) is defined by \({f\mapsto f|f|^{\frac {p-q}q}}\). In analogy with the commutative case, we gather estimates showing that M p,q is \({\min\{\frac pq,1\}}\)-Hölder on balls.
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Ricard, É. Hölder estimates for the noncommutative Mazur maps. Arch. Math. 104, 37–45 (2015). https://doi.org/10.1007/s00013-014-0710-9
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DOI: https://doi.org/10.1007/s00013-014-0710-9