An -type estimate for Riesz potentials

  • Armin Schikorra

    Universität Freiburg, Germany
  • Daniel Spector

    National Chiao Tung University, Hsinchu, Taiwan
  • Jean Van Schaftingen

    Université Catholique de Louvain, Belgium


In this paper we establish new -type estimates for the classical Riesz potentials of order :

This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space and provides a new family of -Sobolev inequalities for the Riesz fractional gradient.

Cite this article

Armin Schikorra, Daniel Spector, Jean Van Schaftingen, An -type estimate for Riesz potentials. Rev. Mat. Iberoam. 33 (2017), no. 1, pp. 291–303

DOI 10.4171/RMI/937