2016-09-152016-09-152015-02Damián 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), 161-181.1069-58691531-5851http://hdl.handle.net/11441/45010In 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Multilinear maximal operatorCalderón-Zygmund theorySharp weighted bounds.info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1007/s00041-014-9364-z