Georgian Mathematical Journal

, Volume 3, Issue 1, pp 81–96 | Cite as

On strong maximal operators corresponding to different frames

  • G. Oniani
Article
  • 15 Downloads

Abstract

The problem is posed and solved whether the conditionsfL(1+1n+L)2(ℝ2) and\(\sup _{\theta \in [0,\pi /2)} \int {_{\{ M_{2,\theta } (f) > 1\} } M_{2,\theta } (f)< \infty } \) are equivalent for functionsfL(ℝ2) (whereM2,ϑ denotes the strong maximal operator corresponding to the frame {OXϑ,OYϑ}).

The results obtained represent a general solution of M. de Guzmán's problem that was previously studied by various authors.

1991 Mathematics Subject Classification

28A15 

Key words and phrases

Strong maximal operators different frames regularity factor of a rectangle 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • G. Oniani
    • 1
  1. 1.Faculty of Mechanics and MathematicsI. Javakhishvili Tbilisi State UniversityTbilisiRepublic of Georgia

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