naa a22 4500 510781411 CHVBK 20180411083248.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11854-013-0030-1 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0030-1 Lerner Andrei Department of Mathematics, Bar-Ilan University, 52900, Ramat Gan, Israel aut On an estimate of Calderón-Zygmund operators by dyadic positive operators [Elektronische Daten] [Andrei Lerner] Given a general dyadic grid D and a sparse family of cubes S = {Q j k ∈ D, define a dyadic positive operator A D,S by $${A_{D,S}}f(x) = \sum\limits_{j,k} {{f_{Q_j^k}}{\chi _{Q_j^k}}} (x)$$ . Given a Banach function space X(ℝ n ) and the maximal Calderón-Zygmund operator $${T_\natural }$$ , we show that $${\left\| {{T_\natural}f} \right\|_X} \leqslant c(T,n)\mathop {\sup }\limits_{D,S} {\left\| {{A_{D,S}}|f|} \right\|_X}$$ 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 "A 2 conjecture”; (iii) an extension of certain mixed A p −A r estimates to general Calderón-Zygmund operators; (iv) an extension of sharp A 1 estimates (known for T ) to the maximal Calderón-Zygmund operator $$\natural $$ . Hebrew University Magnes Press, 2013 Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 141-161 0021-7670 121:1<141 2013 121 11854 https://doi.org/10.1007/s11854-013-0030-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0030-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lerner Andrei Department of Mathematics, Bar-Ilan University, 52900, Ramat Gan, Israel aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 141-161 0021-7670 121:1<141 2013 121 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer