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

DOI: 10.1007/BF02850835

Cite this article as:
Vargas, A.M. Rend. Circ. Mat. Palermo (1995) 44: 273. doi:10.1007/BF02850835


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)


key words and phrases

Maximal Operators

Copyright information

© Springer 1995

Authors and Affiliations

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