Resumen de Endpoint Sobolev and BV continuity for maximal operators, II

José Madrid

• 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.