An L1-type estimate for Riesz potentials

• Armin Schikorra ^[1] ; Daniel Spector ^[2] ; Jean Van Schaftingen ^[3]
  1. [1] University of Freiburg

     University of Freiburg

     Stadtkreis Freiburg im Breisgau, Alemania

     
  2. [2] National Chiao Tung University

     National Chiao Tung University

     Taiwán

     
  3. [3] Université Catholique de Louvain

     Université Catholique de Louvain

     Arrondissement de Nivelles, Bélgica

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 1, 2017, págs. 291-303
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we establish new L1-type estimates for the classical Riesz potentials of order α∈(0,N):

    ∥Iαu∥LN/(N−α)(RN)≤C∥Ru∥L1(RN;RN). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H1(RN) and provides a new family of L1-Sobolev inequalities for the Riesz fractional gradient.