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

Department of Mathematics

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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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

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KW - Zygmund class

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