Rescaled extrapolation for vector-valued functions

Alex Amenta; Emiel Lorist; Mark Veraar

doi:10.5565/PUBLMAT6311905

Rescaled extrapolation for vector-valued functions

Alex Amenta, Emiel Lorist, Mark Veraar

Analysis

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Abstract

We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood-Paley-Rubio de Francia-type estimates and boundedness of variational Carleson operators for Banach function spaces with UMD concavifications.

Original language	English
Pages (from-to)	155-182
Number of pages	28
Journal	Publicacions Matematiques
Volume	63
Issue number	1
DOIs	https://doi.org/10.5565/PUBLMAT6311905
Publication status	Published - 2019

Keywords

Banach function spaces
Extrapolation
Fourier multipliers
Hardy-Littlewood maximal function
Littlewood-Paley-Rubio de Francia inequalities
Muckenhoupt weights
P-convexity
UMD
Variational Carleson operator

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abstract = "We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood-Paley-Rubio de Francia-type estimates and boundedness of variational Carleson operators for Banach function spaces with UMD concavifications.",

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AU - Lorist, Emiel

AU - Veraar, Mark

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AB - We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood-Paley-Rubio de Francia-type estimates and boundedness of variational Carleson operators for Banach function spaces with UMD concavifications.

KW - Banach function spaces

KW - Extrapolation

KW - Fourier multipliers

KW - Hardy-Littlewood maximal function

KW - Littlewood-Paley-Rubio de Francia inequalities

KW - Muckenhoupt weights

KW - P-convexity

KW - UMD

KW - Variational Carleson operator

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JF - Publicacions Matematiques

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Rescaled extrapolation for vector-valued functions

Abstract

Keywords

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