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Characterization of \(H^1\) Sobolev Spaces by Square Functions of Marcinkiewicz Type

  • Shuichi SatoEmail author
Article

Abstract

We establish characterization of \(H^1\) Sobolev spaces by certain square functions of Marcinkiewicz type. The square functions are related to the Lusin area integrals. Also, in the one dimensional case, the non-periodic version of the function of Marcinkiewicz is applied to characterize weighted \(H^1\) Sobolev spaces.

Keywords

Sobolev space Littlewood–Paley function Marcinkiewicz function Lusin area integral 

Mathematics Subject Classification

Primary 46E35 Secondary 42B25 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationKanazawa UniversityKanazawaJapan

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