Rendiconti del Circolo Matematico di Palermo

, Volume 44, Issue 2, pp 273–282

A remark on a maximal function over a Cantor set of directions

  • Ana M. Vargas
Article

Abstract

LetMe0 be the maximal operator over segments of length 1 with directions belonging to a Cantor set. It has been conjectured that this operator is bounded onL2. We consider a sequence of operators over finite sets of directions converging toMe0. We improve the previous estimate for the (L2,L2)-norm of these particular operators. We also prove thatMe0 is bounded from some subsets ofL2 toL2. These subsets are composed of positive functions whose Fourier transforms have a very weak decay or are supported in a vertical strip.

1980 Mathematics Subject Classification (1985 Revision)

42B25 

key words and phrases

Maximal Operators 

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Copyright information

© Springer 1995

Authors and Affiliations

  • Ana M. Vargas
    • 1
  1. 1.Departamento de Matemáticas Facultad de CienciasUniversidad Autónoma de MadridMadridSpain

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