On an estimate of Calderón-Zygmund operators by dyadic positive operators

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Given a general dyadic grid D and a sparse family of cubes S = {Qjk ∈ D, define a dyadic positive operator AD,S by (Formula presented.). Given a Banach function space X(ℝn) and the maximal Calderón-Zygmund operator(Formula presented.) This result is applied to weighted inequalities. In particular, it implies (i) the "twoweight conjecture" by D. Cruz-Uribe and C. Pérez in full generality; (ii) a simplification of the proof of the "A2 conjecture"; (iii) an extension of certain mixed Ap-Ar estimates to general Calderón-Zygmund operators; (iv) an extension of sharp A 1 estimates (known for T) to the maximal Calderón-Zygmund operator T{music natural sign}.

Original languageEnglish
Pages (from-to)141-161
Number of pages21
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - Oct 2013


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