Rescaled extrapolation for vector-valued functions

Alex Amenta; Emiel Lorist; Mark Veraar

doi:10.5565/PUBLMAT6311905

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Home > Journals > Publ. Mat. > Volume 63 > Issue 1 > Article

2019 Rescaled extrapolation for vector-valued functions

Alex Amenta, Emiel Lorist, Mark Veraar

Publ. Mat. 63(1): 155-182 (2019). DOI: 10.5565/PUBLMAT6311905

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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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Alex Amenta. Emiel Lorist. Mark Veraar. "Rescaled extrapolation for vector-valued functions." Publ. Mat. 63 (1) 155 - 182, 2019. https://doi.org/10.5565/PUBLMAT6311905

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Received: 24 March 2017; Revised: 25 October 2017; Published: 2019

First available in Project Euclid: 7 December 2018

zbMATH: 07040965

MathSciNet: MR3908790

Digital Object Identifier: 10.5565/PUBLMAT6311905

Subjects:

Primary: 42B25

Secondary: 42A20 , 42B15 , 42B20 , 46E30

Keywords: $p$-convexity , Banach function spaces , extrapolation , Fourier multipliers , Hardy–Littlewood maximal function , Littlewood–Paley–Rubio de Francia inequalities , Muckenhoupt weights , UMD , variational Carleson operator

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Publ. Mat.

Vol.63 • No. 1 • 2019

Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Alex Amenta, Emiel Lorist, Mark Veraar "Rescaled extrapolation for vector-valued functions," Publicacions Matemàtiques, Publ. Mat. 63(1), 155-182, (2019)

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