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Jean BourgainInstitute for Advanced Study, Olden Lane, Princeton, NJ, USAMichael GoldsteinInstitute for Advanced Study, Olden Lane, Princeton, NJ, USAWilhelm SchlagDivision of Astronomy, Mathematics, and Physics, 253-37 Caltech, Pasadena, CA, USA
A Sobolev space in several variables in an$L$^{1}-type norm is not complemented in its second dual. Hence it is not isomorphic as a Banach space to any complemented subspace of a Banach lattice.