Rearrangement Invariant Norms of Symmetric Sequence Norms of Independent Sequences of Random Variables

Stephen Montgomery-Smith

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Rearrangement Invariant Norms of Symmetric Sequence Norms of Independent Sequences of Random Variables

Stephen Montgomery-Smith

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Abstract

Let X_1, X_2,..., 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 = l_p, and recent work of Gordon, Litvak, Schuett and Werner who obtained similar results for Orlicz spaces.

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BibTeX RIS

Stephen Montgomery-Smith. 2001-07-28. Rearrangement Invariant Norms of Symmetric Sequence Norms of Independent Sequences of Random Variables. https://arxiv.org/abs/math/0106114

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