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. 419–429DOI 10.4171/RMI/787