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A note on the off-diagonal Muckenhoupt-Wheeden conjecture

 

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Opened Access A note on the off-diagonal Muckenhoupt-Wheeden conjecture
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Author: Cruz Uribe, David
Martell Berrocal, José María
Pérez Moreno, Carlos
Coordinator/Director: Navarro Pascual, Juan Carlos
Kaidi Lhachmi, El Amin
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2016
Published in: Advanced Courses of Mathematical Analysis V: Proceedings of the Fifth International School (Universidad de Almería, Almería, Spain, 12-16 September 2011)
ISBN/ISSN: 9789814699686
9789814699709
Document type: Chapter of Book
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 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.
Cite: 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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URI: http://hdl.handle.net/11441/64538

DOI: 10.1142/9789814699693_0006

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