In a recent paper Kato [3] used the Littlewood matrices to
generalise Clarkson's inequalities. Our first aim is to indicate
how Kato's result can be deduced from a neglected version of the
Hausdorff-Young inequality which was proved by Wells and Williams [11].
We next establish "random Clarkson inequalities".. These show that the
expected behaviour of matrices whose coefficients are random ±1's is,
as one might expect, the same as the behaviour that Kato observed in
the Littlewood matrices. Finally we show how sharp LP versions of
Grothendieck's inequality can be obtained by combining a Kato-like
result with a theorem of Bennett [1]on Schur multipliers
