A subscription is required to access this article.
In this paper we study some questions about the continuity of classical and fractional maximal operators in the Sobolev space , 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 from to , for . Here denotes the non-centered fractional maximal operator on , with . The second one is related to the continuity of the discrete centered maximal operator in the space of functions of bounded variation , complementing some recent boundedness results.
Cite this article
José Madrid, Endpoint Sobolev and BV continuity for maximal operators, II. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 2151–2168DOI 10.4171/RMI/1115