Wiener amalgam space

Summary

A Wiener amalgam space measures a function with one norm locally and another norm globally. The basic example $W(L^p, \ell^q)$ takes the $L^p$ norm of the function on each unit cube and then the $\ell^q$ norm of the resulting sequence. Such spaces separate the local regularity of a function from its decay at infinity. They go back to Norbert Wiener, were developed in general by Hans Feichtinger, and are used in time–frequency analysis and sampling theory.