Stephen Montgomery-Smith, Rearrangement Invariant Norms of Symmetric Sequence Norms of Independent Sequences of Random Variables. Israel Journal of Mathematics, 131, (2002), 51-60. Let \(X_1\), \(X_2,\dots,\) \(X_n\) be a sequence of independent random variables, let \(M\) be a rearrangement invariant space on the underlying probability space, and let \(N\) be a symmetric sequence space. This paper gives an approximate formula for the quantity \({\|{\|(X_i)\|}_N\|}_M\) whenever \(L_q\) embeds into \(M\) for some \(1 \le q < \infty\). This extends work of Johnson and Schechtman who tackled the case when \(N = \ell_p\), and recent work of Gordon, Litvak, Schütt and Werner who obtained similar results for Orlicz spaces. (tex, dvi, ps, pdf.)

 

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