J un 1 99 1 A simple proof of a theorem of

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 < r < 1.