2024/06/14 by Narcisse Randrianantoanina, Randrianantoanina, Narcisse
Mathematics · #46L52 #46L53 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2406.10431
openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a semifinite von Neumann algebra equipped with an increasing filtration (Mn)n≥ 1 of (semifinite) von Neumann subalgebras of M. For 1≤ p ≤∞, let Hpc(M) denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration (Mn)n≥ 1 and the index p. We prove the following real interpolation identity: if 0<θ<1 and 1/p=1-θ, then (H1c(M), H_∞c(M))θ,p=Hpc(M). This is new even for classical martingale Hardy spaces as it is previously known only under the assumption that the filtration is regular. We also obtain analogous result for noncommutative column martingale Orlicz-Hardy spaces.