A simple proof of a theorem of Jean Bourgain
Gilles Pisier
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 L1 or L2 is 2-absolutely summing and hence extends to an operator defined on the whole of C. This implies Bourgain's result that L1/H1 is of cotype 2. We also prove more generally that Lr/Hr is of cotype 2 for 0<r< 1.
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