New bounds on cantor maximal operators

• Pablo Shmerkin ^[1] ; Ville Suomala ^[2]
  1. [1] University of British Columbia

     University of British Columbia

     Canadá

     
  2. [2] University of Oulu

     University of Oulu

     Oulu, Finlandia

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 64, Nº. Extra 1, 2022, págs. 69-86
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We prove Lp bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. Laba and M. Pramanik and in some cases are sharp up to the endpoint. A consequence of our main result is that there exist Ahlforsregular Salem Cantor sets of any dimension > 1/2 such that the associated maximal operator is bounded on L2 (R). We follow the overall scheme of Laba– Pramanik for the analytic part of the argument, while the probabilistic part is instead inspired by our earlier work on intersection properties of random measures.