Endpoint Sobolev and BV continuity for maximal operators

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

  • Emanuel Carneiro
  • José Madrid
  • Lillian B. Pierce

Organisaatiot

  • National Institute for Pure and Applied Mathematics
  • Duke University

Kuvaus

In this paper we investigate some questions related to the continuity of maximal operators in W1,1 and BV spaces, complementing some well-known boundedness results. Letting M˜ be the one-dimensional uncentered Hardy–Littlewood maximal operator, we prove that the map f↦(M˜f) is continuous from W1,1(R) to L1(R). In the discrete setting, we prove that M˜:BV(Z)→BV(Z) is also continuous. For the one-dimensional fractional Hardy–Littlewood maximal operator, we prove by means of counterexamples that the corresponding continuity statements do not hold, both in the continuous and discrete settings, and for the centered and uncentered versions.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut3262-3294
Sivumäärä33
JulkaisuJournal of Functional Analysis
Vuosikerta273
Numero10
TilaJulkaistu - 15 marraskuuta 2017
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 17197947