2012/01/03 by Tuomas Hytönen, Hytönen, Tuomas P., Antti V. Vähäkangas +1
Economics, Econometrics and Finance · Mathematics · #42B20 (Primary) 42B25 #46E40 #60G46 (Secondary) #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1201.0648
openalex publication_date 2012/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, `vector-valued' means `taking values in a function lattice with the UMD (unconditional martingale differences) property'. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.