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Sharp weighted bounds for multilinear maximal functions and Calderón-Zygmund operators

 

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Opened Access Sharp weighted bounds for multilinear maximal functions and Calderón-Zygmund operators
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Author: Damián González, Wendolín
Lerner, Andrei K.
Pérez Moreno, Carlos
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2015-02
Published in: Journal of Fourier Analysis and Applications, 21 (1), 161-181.
Document type: Article
Abstract: In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in [18] A.K. Lerner, S. Ombrosi, C. Pérez, R.H. Torres and R. Trujillo-Gonz´alez, New maximal functions and multiple weights for the multilinear Caldern-Zygmund theory, Advances in Math. 220, 1222-1264 (2009). and for multilinear Calderón-Zygmund operators. In particular we obtain a sharp mixed “Ap − A∞” bound for M, some partial results related to a Buckley-type estimate for M, and a sufficient condition for the boundedness of M between weighted Lp spaces with different weights taking into account the precise bounds. Next we get a bound for multilinear Calderón-Zygmund operators in terms of dyadic positive multilinear operators in the spirit of the recent work [16] A.K. Lerner, On an estimate of Calderón-Zygmund operators by dyadic positive operators, J. Anal. Math. Then we obtain a multilinear version of the “A2 conjecture”. Several open problems are posed.
Cite: Damián González, W. y Lerner, A.K. (2015). Sharp weighted bounds for multilinear maximal functions and Calderón-Zygmund operators. Journal of Fourier Analysis and Applications, 21 (1), 161-181.
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URI: http://hdl.handle.net/11441/45010

DOI: 10.1007/s00041-014-9364-z

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