Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales

2009/06/24 by Turdebek N. Bekjan, Zeqian Chen, Bekjan, Turdebek N. +5 · 1 citation
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.0906.4437

openalex publication_date 2009/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that atomic decomposition for the Hardy spaces h₁ and H₁ 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.

Citations

• Interpolation between Hp spaces: The complex method
• Noncommutative Riesz transforms -- a probabilistic approach

Cited by

• Almost uniform convergence for noncommutative Vilenkin-Fourier series

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