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Weighted estimates for the multisublinear maximal function

A formulation of the Carleson embedding theorem in the multilinear setting is proved which allows obtaining a multilinear analogue of Sawyer’s two weight theorem for the multisublinear maximal function $$\mathcal{M }$$ M introduced by Lerner et al. (Adv Math 220:1222–1264, 2009). A multilinear versi... Full description

Journal Title: Rendiconti del Circolo Matematico di Palermo 2013, Vol.62(3), pp.379-391
Main Author: Chen, Wei
Other Authors: Damián, Wendolín
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 0009-725X ; E-ISSN: 1973-4409 ; DOI: 10.1007/s12215-013-0131-9
Link: http://dx.doi.org/10.1007/s12215-013-0131-9
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recordid: springer_jour10.1007/s12215-013-0131-9
title: Weighted estimates for the multisublinear maximal function
format: Article
creator:
  • Chen, Wei
  • Damián, Wendolín
subjects:
  • Multilinear harmonic analysis
  • Multilinear maximal function
  • Weighted norm inequalities
  • Calderón–Zygmund theory
  • Sawyer’s theorem
  • Reverse Hölder inequality
ispartof: Rendiconti del Circolo Matematico di Palermo, 2013, Vol.62(3), pp.379-391
description: A formulation of the Carleson embedding theorem in the multilinear setting is proved which allows obtaining a multilinear analogue of Sawyer’s two weight theorem for the multisublinear maximal function $$\mathcal{M }$$ M introduced by Lerner et al. (Adv Math 220:1222–1264, 2009). A multilinear version of the $$B_p$$ B p theorem from Hytönen and Pérez (Anal PDE, 2013) is also obtained and a mixed $$A_{\overrightarrow{ P}}-W_{\overrightarrow{ P}}^{\infty }$$ A P → - W P → ∞ bound for $$\mathcal{M }$$ M is proved as well.
language: eng
source:
identifier: ISSN: 0009-725X ; E-ISSN: 1973-4409 ; DOI: 10.1007/s12215-013-0131-9
fulltext: fulltext
issn:
  • 1973-4409
  • 19734409
  • 0009-725X
  • 0009725X
url: Link


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subjectMultilinear harmonic analysis ; Multilinear maximal function ; Weighted norm inequalities ; Calderón–Zygmund theory ; Sawyer’s theorem ; Reverse Hölder inequality
descriptionA formulation of the Carleson embedding theorem in the multilinear setting is proved which allows obtaining a multilinear analogue of Sawyer’s two weight theorem for the multisublinear maximal function $$\mathcal{M }$$ M introduced by Lerner et al. (Adv Math 220:1222–1264, 2009). A multilinear version of the $$B_p$$ B p theorem from Hytönen and Pérez (Anal PDE, 2013) is also obtained and a mixed $$A_{\overrightarrow{ P}}-W_{\overrightarrow{ P}}^{\infty }$$ A P → - W P → ∞ bound for $$\mathcal{M }$$ M is proved as well.
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abstractA formulation of the Carleson embedding theorem in the multilinear setting is proved which allows obtaining a multilinear analogue of Sawyer’s two weight theorem for the multisublinear maximal function $$\mathcal{M }$$ M introduced by Lerner et al. (Adv Math 220:1222–1264, 2009). A multilinear version of the $$B_p$$ B p theorem from Hytönen and Pérez (Anal PDE, 2013) is also obtained and a mixed $$A_{\overrightarrow{ P}}-W_{\overrightarrow{ P}}^{\infty }$$ A P → - W P → ∞ bound for $$\mathcal{M }$$ M is proved as well.
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doi10.1007/s12215-013-0131-9
pages379-391
date2013-12