Georgian Mathematical Journal

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

On strong maximal operators corresponding to different frames

  • G. Oniani


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


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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