Endpoint Sobolev and BV continuity for maximal operators, II

• José Madrid ^[1]
  1. [1] University of California Los Angeles

     University of California Los Angeles

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 7, 2019, págs. 2151-2168
• Idioma: inglés
• DOI: 10.4171/rmi/1115
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we study some questions about the continuity of classical and fractional maximal operators in the Sobolev space W1,1, in both the continuous and discrete setting, giving a positive answer to two questions posed recently, one of them regarding the continuity of the map f↦(M˜βf)′ from W1,1(R) to Lq(R), for q=1/(1−β). Here M˜β denotes the non-centered fractional maximal operator on R, with β∈(0,1). The second one is related to the continuity of the discrete centered maximal operator in the space of functions of bounded variation BV(Z), complementing some recent boundedness results.