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Czechoslovak Mathematical Journal

, Volume 69, Issue 2, pp 337–351 | Cite as

Boundedness of Littlewood-Paley operators relative to non-isotropic dilations

  • Shuichi SatoEmail author
Article
  • 54 Downloads

Abstract

We consider Littlewood-Paley functions associated with a non-isotropic dilation group on ℝn. We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted Lp spaces, 1 < p < ∞, with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).

Keywords

Littlewood-Paley function non-isotropic dilation 

MSC 2010

42B25 46E30 

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Copyright information

© Mathematical Institute, Academy of Sciences of Cz 2019

Authors and Affiliations

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

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