Two-sided bounds for LpLp-norms of combinations of products of independent random variables

We show that for every positive pp, the LpLp-norm of linear combinations (with scalar or vector coefficients) of products of i.i.d. random variables, whose moduli have a nondegenerate distribution with the pp-norm one, is comparable to the lplp-norm of the coefficients and the constants are explicit. As a result the same holds for linear combinations of Riesz products.We also establish the upper and lower bounds of the LpLp-moments of partial sums of perpetuities.