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 socalled 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 onevariable endpoint offdiagonal 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 mixednorm estimates for tensor products of bilinear Calder'onZygmund operators with a proof based on extrapolation and on some estimates with weights in some mixednorm classes. The same occurs with the multilinear Calder'onZygmund 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 vectorvalued inequalities with multilinear weights and these include the endpoint cases.
Original language  English 

Journal  Transactions of the American Mathematical Society 
Volume  374 
Issue number  1 
Pages (fromto)  97135 
Number of pages  39 
ISSN  00029947 
DOIs  
Publication status  Published  Jan 2021 
MoE publication type  A1 Journal articlerefereed 
Fields of Science
 111 Mathematics
 Multilinear Muckenhoupt weights
 Rubio de Francia extrapolation
 multilinear Calder'onZygmund operators
 bilinear Hilbert transform
 vectorvalued inequalities
 mixednorm estimates
 WEIGHTED NORM INEQUALITIES
 SINGULARINTEGRALS
 VALUED INEQUALITIES
Projects
 2 Finished

Singular integrals and the geometry of measures
Martikainen, H. & Oikari, T.
Valtion perusrahoitus/hankkeet
01/01/2018 → 31/12/2020
Project: University of Helsinki ThreeYear Research Project

Geometric and dyadic harmonic analysis: general measures and rectifiability
Martikainen, H. & Airta, E.
01/09/2016 → 31/08/2021
Project: Research project