Best constant in the decoupling inequality for non-negative random variables

A simple proof of the following inequality is given: ||[summation operator]Xk||>p [less-than-or-equals, slant] 3p||[summation operator]yk||p, p [greater-or-equal, slanted] 1, where, for n [greater-or-equal, slanted] 1, Xn and Yn are Fn-measurable non-negative random variables with indentical conditional distributions, given Fn-1. Our proof gives the best possible order of constant.