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 isf0 ⩾ 0 with (1 + ¦υ¦2)φ0 εL1 and (1 + ¦υ¦)sf0ε L∞ for somes > 2, then (1 + ¦υ¦s'ftεL∞ fort>0 and essυ,tsup(1 + ¦υ¦)s'f(υ, t,) < ∞ for anys′ ⩽ s whens ⩽ 5, and anys′ ⩽ s ifs > 5.