TY - JOUR
T1 - On an estimate of Calderón-Zygmund operators by dyadic positive operators
AU - Lerner, Andrei K.
PY - 2013/10
Y1 - 2013/10
N2 - 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}.
AB - 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}.
UR - http://www.scopus.com/inward/record.url?scp=84888022598&partnerID=8YFLogxK
U2 - 10.1007/s11854-013-0030-1
DO - 10.1007/s11854-013-0030-1
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AN - SCOPUS:84888022598
SN - 0021-7670
VL - 121
SP - 141
EP - 161
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -