RT Journal Article
T1 Extrapolation for multilinear Muckenhoupt classes and applications
A1 Li, Kangwei
A1 Martell, José María
A1 Ombrosi, Sheldy Javier
AB In this paper we solve a long standing problem about the multivariable Rubio de Francia extrapolation theorem for the multilinear Muckenhoupt classes, which were extensively studied by Lerner et al. and which are the natural ones for the class of multilinear Calderón-Zygmund operators as well as for some bilinear rough singular integral operators. Furthermore, we go beyond the classes and extrapolate within the classes which appear naturally associated to the weighted norm inequalities for multilinear sparse forms which control fundamental operators such as the bilinear Hilbert transform. We give several applications which can be easily obtained using extrapolation. First, weighted norm inequalities (scalar and vector-valued) for the bilinear rough singular integral operators are established. Second, for the bilinear Hilbert transform one can extrapolate from the recent result of Culiuc et al. who considered the Banach range, extend the estimates to the quasi-Banach range, and furthermore, prove trivially vector-valued inequalities. We also extend recent results of Carando et al. on Marcinkiewicz-Zygmund estimates for multilinear Calderón-Zygmund operators. Finally, our last application gives new weighted estimates (scalar and vector-valued) for the commutators of multilinear Calderón-Zygmund operators, bilinear rough singular integral operators, and for the bilinear Hilbert transform with BMO functions using ideas from Bényi et al.
PB Elsevier
SN 0001-8708
YR 2020
FD 2020
LK https://hdl.handle.net/20.500.14352/98562
UL https://hdl.handle.net/20.500.14352/98562
LA eng
NO K. Li, J.M. Martell, S. Ombrosi, Extrapolation for multilinear Muckenhoupt classes and applications, Advances in Mathematics 373 (2020) 107286. https://doi.org/10.1016/j.aim.2020.107286.
DS Docta Complutense
RD 8 abr 2025