The vector-valued non-homogeneous Tb theorem

2008/09/18 by Tuomas Hytönen, Hytönen, Tuomas
Mathematics · #42B20 #42B25 #46B09 #46E40 #60G46 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.0809.3097

openalex publication_date 2008/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

The paper gives a Banach space -valued extension of the Tb theorem of Nazarov, Treil and Volberg (2003) concerning the boundedness of singular integral operators with respect to a measure, which only satisfies an upper control on the size of balls. Under the same assumptions as in their result, such operators are shown to be bounded on the Bochner spaces of functions with values in a Banach space with the unconditionality property of martingale differences (UMD). The new proof deals directly with all Lebesgue exponents p in the range 1

Related

• The local non-homogeneous Tb theorem for vector-valued functions
• On singular integral and martingale transforms
• An operator-valued T(1) theorem for symmetric singular integrals in UMD spaces
• The Tb-theorem on non-homogeneous spaces that proves a conjecture of Vitushkin
• On Azuma-type inequalities for Banach space-valued martingales