The structure of Sobolev extension operators

  • Charles Fefferman

    Princeton University, United States
  • Arie Israel

    University of Texas at Austin, USA
  • Garving K. Luli

    University of California at Davis, USA


Let denote the Sobolev space of functions whose -th derivatives lie in , and assume that . For , denote by the space of restrictions to of functions . It is known that there exist bounded linear maps such that on for any . We show that cannot have a simple form called “bounded depth”.

Cite this article

Charles Fefferman, Arie Israel, Garving K. Luli, The structure of Sobolev extension operators. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 419–429

DOI 10.4171/RMI/787