Tangent Sequences in Orlicz and Rearrangement Invariant Spaces

Details Tangent Sequences in Orlicz and Rearrangement Invariant Spaces Tangent Sequences in Orlicz and Rearrangement Invariant Spaces

1994-06-07

arxiv.org/abs/math/9406213v2

Proc. Camb. Phil. Soc. 119, (1996), 91-101

Mathematics

Functional Analysis

Scientific paper

Let (f_n) and (g_n) be two sequences of random variables adapted to an increasing sequence of $\sigma$-algebras $({\cal F}_n)$ such that the conditional distributions of f_n and g_n given ${\cal F}_{n-1}$ coincide, and such that the sequence (g_n) is conditionally independent. Then it is known that $\normo{\sum f_k}_p \le C \normo{\sum g_k}_p$, $1 \le p \le \infty$ where the constant C is independent of p. The aim of this paper is to extend this result to certain classes of Orlicz and rearrangement invariant spaces. This paper includes fairly general techniques for obtaining rearrangement invariant inequalities from Orlicz norm inequalities.

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