End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
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- by Kangwei Li, José María Martell, Henri Martikainen, Sheldy Ombrosi and Emil Vuorinen PDF
- Trans. Amer. Math. Soc. 374 (2021), 97-135 Request permission
Abstract:
In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. Here we consider the situations where some of the exponents of the Lebesgue spaces appearing in the hypotheses and/or in the conclusion can be possibly infinity. The scheme we follow is similar, but, in doing so, we need to develop a one-variable end-point off-diagonal extrapolation result. This complements the corresponding “finite” case obtained by Duoandikoetxea, which was one of the main tools in the aforementioned paper. The second goal of this paper is to present some applications. For example, we obtain the full range of mixed-norm estimates for tensor products of bilinear Calderón-Zygmund operators with a proof based on extrapolation and on some estimates with weights in some mixed-norm classes. The same occurs with the multilinear Calderón-Zygmund operators, the bilinear Hilbert transform, and the corresponding commutators with BMO functions. Extrapolation along with the already established weighted norm inequalities easily give scalar and vector-valued inequalities with multilinear weights and these include the end-point cases.References
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Additional Information
- Kangwei Li
- Affiliation: BCAM, Basque Center for Applied Mathematics, Mazarredo 14, E-48009 Bilbao, Spain
- Address at time of publication: Center for Applied Mathematics, Tianjin University, Weijin Road 92, 300072 Tianjin, People’s Republic of China
- MR Author ID: 977289
- Email: kli@tju.edu.cn
- José María Martell
- Affiliation: Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13-15, E-28049 Madrid, Spain
- MR Author ID: 671782
- ORCID: 0000-0001-6788-4769
- Email: chema.martell@icmat.es
- Henri Martikainen
- Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, FI-00014 University of Helsinki, Finland
- MR Author ID: 963282
- Email: henri.martikainen@helsinki.fi
- Sheldy Ombrosi
- Affiliation: Department of Mathematics, Universidad Nacional del Sur, Bahía Blanca, Argentina
- MR Author ID: 713193
- Email: sombrosi@uns.edu.ar
- Emil Vuorinen
- Affiliation: Centre for Mathematical Sciences, University of Lund, P.O.B. 118, 22100 Lund, Sweden
- MR Author ID: 1178205
- ORCID: 0000-0001-8986-0725
- Email: j.e.vuorin@gmail.com
- Received by editor(s): February 15, 2019
- Received by editor(s) in revised form: March 9, 2020
- Published electronically: October 20, 2020
- Additional Notes: The first author was supported by Juan de la Cierva - Formación 2015 FJCI-2015-24547, by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2017-0718, and through project MTM2017-82160-C2-1-P funded by (AEI/FEDER, UE) and acronym “HAQMEC”
The second author was supported by the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554) and the European Research Council through the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC agreement no. 615112 HAPDEGMT
The third author was supported by the Academy of Finland through the grants 294840 and 306901, and by the three-year research grant 75160010 of the University of Helsinki. He is a member of the Finnish Centre of Excellence in Analysis and Dynamics Research
The fourth author was supported by CONICET PIP 11220130100329CO, Argentina.
The fifth author was supported by the Jenny and Antti Wihuri Foundation. - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 97-135
- MSC (2010): Primary 42B20, 42B25, 42B35
- DOI: https://doi.org/10.1090/tran/8172
- MathSciNet review: 4188179