In principle, there are three different mathematical frameworks developed for the Boltzmann equation.They are the theories in the L1, L2, and L∞ spaces.Even though their principal ideas and methods are different, they have been successfully used to establish the existence theorems of global solutions with various deep structures.For the further development, however, it will be fairly desirable to merge these different frameworks and methods.In this talk, as an attempt in this direction, we present a result on the optimalconvergence rate to the stationary solution for the Boltzmann equation with a potential force by combining the analytic techniques used in L∞ and L2 frameworks.The result arises from the joint project with Renjun Duan, Seiji Ukai and Huijiang Zhao.