Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales

TL;DR

This paper extends atomic decomposition and interpolation properties to Hardy spaces of noncommutative martingales, advancing the understanding of their structure and functional analysis.

Contribution

It proves atomic decomposition for noncommutative Hardy spaces and establishes interpolation scales for conditioned Hardy spaces and BMO.

Findings

Atomic decomposition holds for h_1 and H_1 noncommutative martingale Hardy spaces.

Conditioned Hardy spaces h_p and bmo form interpolation scales.

Results apply to both complex and real interpolation methods.

Abstract

We prove that atomic decomposition for the Hardy spaces h_1 and H_1 is valid for noncommutative martingales. We also establish that the conditioned Hardy spaces of noncommutative martingales h_p and bmo form interpolation scales with respect to both complex and real interpolations.