Two-sided moment estimates for a class of nonnegative chaoses

We derive two-sided bounds for moments of random multi-linear forms (random chaoses) with nonnegative coefficients generated by independent nonnegative random variables XiXi which satisfy the following condition on the growth of moments: ‖Xi‖2p≤A‖Xi‖p‖Xi‖2p≤A‖Xi‖p for any ii and p≥1p≥1. The estimates are deterministic and exact up to multiplicative constants which depend only on the order of chaos and the constant AA in the moment assumption.