Order of magnitude bounds for expectations of \(\Delta_2\)-functions of generalized random bilinear forms (Q1281417)

The object of this paper is to construct two sided bounds for moments (and integrals of more general functions) of general bilinear forms in arbitrary independent random variables. By decoupling results of \textit{V. H. de la Peña} and \textit{S. J. Montgomery-Smith} [Ann. Probab. 23, No. 2, 806-816 (1995; Zbl 0827.60014)] it suffices to consider decoupled forms, and then, by methods developed in this paper, including iteration of Khinchin's inequality, it suffices to consider decoupled nonnegative bilinear forms of nonnegative random variables, which were treated in a previous paper by the authors [ibid. 25, No. 3, 1471-1501 (1997; Zbl 0895.60018)].