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Martingale inequalities and Operator space structures on
We describe a new operator space structure on when is an even
integer and compare it with the one introduced in our previous work using
complex interpolation. For the new structure, the Khintchine inequalities and
Burkholder's martingale inequalities have a very natural form:\ the span of the
Rademacher functions is completely isomorphic to the operator Hilbert space
, and the square function of a martingale difference sequence is
. Various inequalities from harmonic analysis are
also considered in the same operator valued framework. Moreover, the new
operator space structure also makes sense for non commutative -spaces with
analogous results.Comment: Minor corrections. Paper will appear in Documenta Mat
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