A simple proof of a theorem of Jean Bourgain. Academic Article uri icon

abstract

  • We give a simple proof of Bourgain's disc algebra version of Grothendieck's theorem, i.e. that every operator on the disc algebra with values in $L_1$ or $L_2$ is 2-absolutely summing and hence extends to an operator defined on the whole of $C$. This implies Bourgain's result that $L_1/H^1$ is of cotype 2. We also prove more generally that $L_r/H^r$ is of cotype 2 for $0

published proceedings

  • The Michigan Mathematical Journal

author list (cited authors)

  • Pisier, G.

citation count

  • 5

complete list of authors

  • Pisier, G

publication date

  • January 1, 1992 11:11 AM