Projects per year
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 Calder'on-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 Calder'on-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.
Original language | English |
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Journal | Transactions of the American Mathematical Society |
Volume | 374 |
Issue number | 1 |
Pages (from-to) | 97-135 |
Number of pages | 39 |
ISSN | 0002-9947 |
DOIs | |
Publication status | Published - Jan 2021 |
MoE publication type | A1 Journal article-refereed |
Fields of Science
- 111 Mathematics
- Multilinear Muckenhoupt weights
- Rubio de Francia extrapolation
- multilinear Calder'on-Zygmund operators
- bilinear Hilbert transform
- vector-valued inequalities
- mixed-norm estimates
- WEIGHTED NORM INEQUALITIES
- SINGULAR-INTEGRALS
- VALUED INEQUALITIES
Projects
- 2 Finished
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Singular integrals and the geometry of measures
Martikainen, H. (Project manager) & Oikari, T. (Participant)
Valtion perusrahoitus/hankkeet
01/01/2018 → 31/12/2020
Project: University of Helsinki Three-Year Research Project
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Geometric and dyadic harmonic analysis: general measures and rectifiability
Martikainen, H. (Project manager) & Airta, E. (Participant)
01/09/2016 → 31/08/2021
Project: Research project