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A note on the off-diagonal Muckenhoupt-Wheeden conjecture
Author/s | Cruz Uribe, David
Martell Berrocal, José María Pérez Moreno, Carlos |
Editor | Navarro Pascual, Juan Carlos
Kaidi Lhachmi, El Amin |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Date | 2016 |
Published in |
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ISBN/ISSN | 9789814699686 9789814699709 |
Abstract | We obtain the off-diagonal Muckenhoupt-Wheeden conjec-ture for Calder´on-Zygmund operators. Namely, given 1 < p < q < ∞ and a pair of weights (u, v), if the Hardy-Littlewood maximal functionsatisfies the following two weight ... We obtain the off-diagonal Muckenhoupt-Wheeden conjec-ture for Calder´on-Zygmund operators. Namely, given 1 < p < q < ∞ and a pair of weights (u, v), if the Hardy-Littlewood maximal functionsatisfies the following two weight inequalities: M : Lp(v) → Lq(u) and M : Lq´(u1−q´) → Lp´(v1−p´), then any Calderón-Zygmund operator Tand its associated truncatedmaximal operator T⋆ are bounded from Lp(v) to Lq(u). Additionally, as-suming only the second estimate for Mthen Tand T* map continuouslyLp(v) into Lq,∞(u). We also consider the case of generalized Haar shiftoperators and show that their off-diagonal two weight estimates are gov-erned by the corresponding estimates for the dyadic Hardy-Littlewoodmaximal function. |
Citation | Cruz Uribe, D., Martell Berrocal, J.M., y Pérez Moreno, C. (2016). A note on the off-diagonal Muckenhoupt-Wheeden conjecture. En E.A. Kaidi Lhachmi, J.C. Navarro Pascual (Ed.), Advanced Courses of Mathematical Analysis V: Proceedings of the Fifth International School (Universidad de Almería, Almería, Spain, 12-16 September 2011) (pp. 244-252). World Scientific |
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