Operator-valued dyadic BMO spaces

2008/05/01 by Óscar Blasco, Oscar Blasco, Sandra Pott +2
Mathematics · #42B30 #42B35 (Primary) #47B35 (Secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.FA #msc:42B30 #msc:42B35 #msc:47B35

paper · pdf · doi:10.48550/arxiv.0805.0158

to appear in J. Operator Theory

arxiv created 2008/05/01 · openalex publication_date 2008/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions B which define a bounded paraproduct on L²(H). We obtain several equivalent formulations of ‖π_B‖ in terms of the norm of the "sweep" function of B or of averages of the norms of martingales transforms of B in related spaces. Furthermore, we investigate a connection between John-Nirenberg type inequalities and Carleson-type inequalities via a product formula for paraproducts and deduce sharp dimensional estimates for John-Nirenberg type inequalities.

Related

• Embeddings between operator-valued dyadic BMO spaces
• The Banach space -valued BMO, Carleson's condition, and paraproducts
• Notes on Matrix Valued Paraproducts
• On two weight estimates for dyadic operators
• Logarithmic mean oscillation on the polydisc, endpoint results for multi-parameter paraproducts, and commutators on BMO