The T(b) Theorem of Nazarov, Treil, and Volberg

Part of the Universitext book series (UTX)


The goal of this long chapter is to prove Theorem 6.14, the first of the two difficult results needed to complete the resolution of Vitushkin’s Conjecture. Our treatment here, and in various parts of the previous chapter, is from [NTV].


Doubling Condition Bellman Function Standard Decomposition Covering Lemma Trivial Covering 
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  1. [NT]
    F. Nazarov and S. Treil, The hunt for a Bellman function, Algebra i Analiz, Vol. 8 (1996), 32–162. ( Section 7.6)MathSciNetMATHGoogle Scholar
  2. [NTV]
    F. Nazarov, S. Treil, and A. Volberg, The Tb-theorem on non-homogeneous spaces that proves a conjecture of Vitushkin, Preprint No. 519, Center de Recerca Matemàtica, Barcelona, 2002. ( Sections 6.5 and  7.1)Google Scholar
  3. [RUD]
    W. Rudin, Real and Complex Analysis, 3rd Edition, McGraw-Hill Book Company (1987). (Preface and Many Sections)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Lyman Briggs College, Michigan State UniversityEast LansingUSA

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