A simple proof of a theorem of Jean Bourgain

Details A simple proof of a theorem of Jean Bourgain A simple proof of a theorem of Jean Bourgain

1991-06-03

arxiv.org/abs/math/9201228v1

Mathematics

Functional Analysis

Scientific paper

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

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