L ∞ estimates for the space-homogeneous Boltzmann equation

This paper studies the boundedness of solutionsf of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, whenk>5, and under angular cutoff. The main result is that if the initial value isf ₀ ? 0 with (1 + ¦υ¦²)φ₀ εL ¹ and (1 + ¦υ¦)^s f ₀ε L^∞ for somes > 2, then (1 + ¦υ¦^s'f _tεL ^∞ fort>0 and ess_υ,t sup(1 + ¦υ¦)^s'f(υ, t,) < ∞ for anys′ ? s whens ? 5, and anys′ ? s ifs > 5.