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• W2047257705 abstract "Given a general dyadic grid D and a sparse family of cubes S = {Q k j ∈ D, define a dyadic positive operator A D,S by $${A_{D,S}}f(x) = sumlimits_{j,k} {{f_{Q_j^k}}{chi _{Q_j^k}}} (x)$$. Given a Banach function space X(ℝn) 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 )." @default.
• W2047257705 created "2016-06-24" @default.
• W2047257705 creator A5052348585 @default.
• W2047257705 date "2013-10-01" @default.
• W2047257705 modified "2023-10-13" @default.
• W2047257705 title "On an estimate of Calderón-Zygmund operators by dyadic positive operators" @default.
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• W2047257705 doi "https://doi.org/10.1007/s11854-013-0030-1" @default.
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