Algebraic Calderón-Zygmund theory

Runlian Xia (ICMAT)

Thursday 16th May 16:00-17:00 Maths 311B

Abstract

In the classical harmonic analysis, Calderón-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we present a new approach for general measure spaces (von Neumann algebras) which admit a Markov semigroup satisfying purely algebraic assumptions. We shall construct an abstract form of ‘Markov metric’ governing the Markov process and the naturally associated BMO spaces, which interpolate with the Lp-scale and admit endpoint inequalities for Calderón-Zygmund operators. Joint work with Marius Junge, Tao Mei and Javier Parcet.

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