Multilinear Forms and Measures of Dependence between Random Variables
نویسنده
چکیده
In his studies of mixing conditions on Markov chains, Rosenblatt [32; 33, Chap. 71 used the Riesz convexity (interpolation) theorem to compare different measures of dependence between two given families of random variables on a probability space. Rosenblatt [34] also suggested that by using other results in operator theory, one might be able to obtain more information about the relationships between various measures of dependence. In this article we shall follow up this suggestion and, in essence, see what more information can be obtained from the Riesz-Thorin and Marcinkiewicz interpolation theorems and from a key idea of Stein and Weiss c371. The nature of this paper is partly expository, pointing out relevant
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