On square functions with independent increments and Sobolev spaces on the line

Julià Cufí; Artur Nicolau; Andreas Seeger; Joan Verdera

doi:10.1007/s10231-017-0709-5

On square functions with independent increments and Sobolev spaces on the line

Julià Cufí, Artur Nicolau, Andreas Seeger, Joan Verdera

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany. We prove a characterization of some Lp-Sobolev spaces involving the quadratic symmetrization of the Calderón commutator kernel, which is related to a square function with differences of difference quotients. An endpoint weak type estimate is established for functions in homogeneous Hardy–Sobolev spaces H˙α1. We also use a local version of this square function to characterize pointwise differentiability for functions in the Zygmund class.

Original language	English
Pages (from-to)	905-940
Journal	Annali di Matematica Pura ed Applicata
Volume	197
Issue number	3
DOIs	https://doi.org/10.1007/s10231-017-0709-5
Publication status	Published - 1 Jun 2018

Keywords

Hardy space
Sobolev space
Square function
Zygmund class

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10.1007/s10231-017-0709-5

Aspectos probabilísticos y geométricos de la teoría de funciones
Nicolau Nos, A., Gonzalez Llorente, J., Arroyo Garcia, A. R., Donaire Benito, J. J., Soler Gibert, O., González Fuentes, M. J., Levi, M., Limani, A. & Macia Medina, V. J.
Ministerio de Ciencia e Innovación (MICINN)
1/01/18 → 30/09/22
Project: Research Projects and Other Grants

Cite this

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title = "On square functions with independent increments and Sobolev spaces on the line",

abstract = "{\textcopyright} 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany. We prove a characterization of some Lp-Sobolev spaces involving the quadratic symmetrization of the Calder{\'o}n commutator kernel, which is related to a square function with differences of difference quotients. An endpoint weak type estimate is established for functions in homogeneous Hardy–Sobolev spaces H˙α1. We also use a local version of this square function to characterize pointwise differentiability for functions in the Zygmund class.",

keywords = "Hardy space, Sobolev space, Square function, Zygmund class",

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AU - Cufí, Julià

AU - Nicolau, Artur

AU - Seeger, Andreas

AU - Verdera, Joan

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N2 - © 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany. We prove a characterization of some Lp-Sobolev spaces involving the quadratic symmetrization of the Calderón commutator kernel, which is related to a square function with differences of difference quotients. An endpoint weak type estimate is established for functions in homogeneous Hardy–Sobolev spaces H˙α1. We also use a local version of this square function to characterize pointwise differentiability for functions in the Zygmund class.

AB - © 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany. We prove a characterization of some Lp-Sobolev spaces involving the quadratic symmetrization of the Calderón commutator kernel, which is related to a square function with differences of difference quotients. An endpoint weak type estimate is established for functions in homogeneous Hardy–Sobolev spaces H˙α1. We also use a local version of this square function to characterize pointwise differentiability for functions in the Zygmund class.

KW - Hardy space

KW - Sobolev space

KW - Square function

KW - Zygmund class

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DO - 10.1007/s10231-017-0709-5

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JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 3

ER -

On square functions with independent increments and Sobolev spaces on the line

Abstract

Keywords

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Aspectos probabilísticos y geométricos de la teoría de funciones

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