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  "body": "\n## Summary\n\nA Wiener amalgam space measures a function with one norm locally and another norm globally.\nThe 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.\nSuch spaces separate the local regularity of a function from its decay at infinity.\nThey go back to Norbert Wiener, were developed in general by Hans Feichtinger, and are used in [[time–frequency analysis|GQFPVXEWK1]] and sampling theory.\n\n## Explanations\n\n### L1 human\n\nCut the line or the space into unit cubes.\nOn each cube, measure the function with one ruler, for instance its largest value.\nThen add up these local sizes over all cubes with a second ruler.\nA function with tall but narrow spikes can fail the local test, and a function with slow decay can fail the global test.\nFor example, $1/(1 + \\abs{x})$ on the line has local maxima about $1/\\abs{k}$ on the cube near $k$, so its sizes have finite sum of squares but infinite plain sum.\n",
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