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arXiv · 2604.23864

Bourgain's method for K-closedness in the semicommmutative setting

Hugues Moyart
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Abstract

In the early 1990s, J.Bourgain proved a general result $K$-closedness result in the context of classical harmonic analysis. In this paper, we extend Bourgain's method to the semicommutative setting, making use of the recent semicommutative Calder\'on-Zygmund decomposition introduced by L.Cadilhac, JM.Conde-Alonso and J.Parcet. As an application, we recover Pisier's result about $K$-closedness of noncommutative Hardy spaces on the torus, and we also establish new interpolation results for noncommutative Sobolev spaces on the torus.

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Hugues Moyart. 2026-04-26. Bourgain's method for K-closedness in the semicommmutative setting. https://arxiv.org/abs/2604.23864

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