#### When do \[\small\lfloor \frac n2\rfloor + 1\] Derivatives suffice in the Mikhlin Multiplier Theorem?

**Marius Junge**(University of Illinois at Urbana-Champaign)

Viernes, 6 de noviembre, Dpto. Matemáticas UAM, Módulo 17, aula 520, 12:30 |

**Abstract:**

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The Mikhlin multiplier theorem is arguably one of the most basic results in classical harmonic analysis. A vector-valued form was obtained by Girardi-Weiss based on the fundamental work of Burkholder and Bourgain on spaces with unconditional martingale differences, so-called UMD spaces. More recently Hytönen has improved their result and also conjectured that \[\small\lfloor \frac n2\rfloor + 1\]

derivatives suffice for all UMD spaces. We will investigate Mikhlin multiplier theorem from a noncommutative angle to prove Hytönen’s conjecture assuming unconditionality of noncommutative martingale differences. In the talk, it will be explained why it suffices to consider very simple commutation relations which are well-understood in noncommutative geometry. This is joint work with Tao Mei and Javier Parcet.