The thesis is divided into three parts. It includes a brief introduction of
the collision kernel, and the uses of the tools in X. Lu, C. Mouhot, to derive
the result for a solution of spatially homogeneous Boltzmann equation in
Lebesgue p-integrable space with finite initial moment and makes it to be
controlled by an exponentially like function as time goes on. And after the
conclusion comes along some appendices which make the thesis more clear
on its way to the final work.