End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications

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Li , K , Martell , J M , Martikainen , H , Ombrosi , S & Vuorinen , E 2021 , ' End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications ' , Transactions of the American Mathematical Society , vol. 374 , no. 1 , pp. 97-135 . https://doi.org/10.1090/tran/8172

Title: End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
Author: Li, Kangwei; Martell, José María; Martikainen, Henri; Ombrosi, Sheldy; Vuorinen, Emil
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2021-01
Language: eng
Number of pages: 39
Belongs to series: Transactions of the American Mathematical Society
ISSN: 0002-9947
URI: http://hdl.handle.net/10138/327173
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.
Subject: 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
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