TY - JOUR
T1 - Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators
AU - Damián, Wendolín
AU - Lerner, Andrei K.
AU - Pérez, Carlos
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2015/2
Y1 - 2015/2
N2 - In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in Lerner et al. (Adv 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 (Lerner, J Anal Math 121:141–161, 2013). Then we obtain a multilinear version of the “A2 conjecture”. Several open problems are posed.
AB - In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in Lerner et al. (Adv 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 (Lerner, J Anal Math 121:141–161, 2013). Then we obtain a multilinear version of the “A2 conjecture”. Several open problems are posed.
KW - Calderón–Zygmund theory
KW - Multilinear maximal operator
KW - Sharp weighted bounds
UR - http://www.scopus.com/inward/record.url?scp=84943589324&partnerID=8YFLogxK
U2 - 10.1007/s00041-014-9364-z
DO - 10.1007/s00041-014-9364-z
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AN - SCOPUS:84943589324
SN - 1069-5869
VL - 21
SP - 161
EP - 181
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 1
ER -