Article

Journal d'Analyse Mathématique

, Volume 111, Issue 1, pp 369-390

The discrete maximal operator in metric spaces

  • Daniel AaltoAffiliated withDepartment of Mathematics, University of Turku Email author 
  • , Juha KinnunenAffiliated withInstitute of Mathematics, Helsinki University of Technology

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Abstract

We study the action of the so-called discrete maximal operator on Newtonian, Hölder and BMO spaces on metric measure spaces equipped with a doubling measure and a Poincaré inequality. The discrete maximal operator has better regularity properties than the standard Hardy-Littlewood maximal operator and hence is a more flexible tool in this context.