arXiv subjects

Hugues Moyart

Publications and source records attributed to Hugues Moyart.

3 recordsLinked to original sources

arXiv2026

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

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.

math.FA↗

arXiv2026

A note on Pisier's method in interpolation of abstract Hardy spaces

In his approach to Jones theorem on the interpolation of Hardy spaces on the torus, Pisier introduced an original method allowing the computation of complex interpolation spaces by means of real interpolation techniques. This approach has been successfully extended to noncommutative analytic Hardy spaces arising from subdiagonal algebras. In this paper, we formulate and prove an abstract version of Pisier s method in a more general setting. The method is then applied in the study of noncommutative martingale transforms.

math.FA↗

arXiv2024

K-closedness results in noncommutative Lebesgue spaces with filtrations

In this paper, we establish a new general $K$-closedness result in the context of real interpolation of noncommutative Lebesgue spaces involving filtrations. As an application, we derive $K$-closedness results for various classes of noncommutative martingale Hardy spaces, addressing a problem raised by Randrianantoanina. The proof of this general result adapts Bourgain's approach to the real interpolation of classical Hardy spaces on the disk within the framework of noncommutative martingales.

math.OA↗