Besov space

Summary

A Besov space $B^s_{p,q}(\R^n)$ is a space of functions or tempered distributions that measures smoothness of order $s$ in the $L^p$ sense. A third index $q$ gives a fine tuning. It is defined by cutting the Fourier transform of a function into dyadic frequency shells and measuring each piece in $L^p$. Besov spaces contain many classical spaces, such as Hölder spaces and fractional Sobolev spaces, and they are stable under real interpolation. They appear naturally as spaces of boundary values of Sobolev functions and in the study of nonlinear evolution equations.