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  "body": "\n## Summary\n\nA harmonic majorant of a function is a [[harmonic function|0DEB0JMN0W]] that lies above it everywhere on the domain.\nThe question whether a [[subharmonic function|Z1MHMGFNFW]] has a harmonic majorant measures how large it is near the boundary of its domain.\nFor example, a holomorphic function $f$ on the unit disc lies in the [[Hardy space|PNNNFJVF6W]] $H^p$ exactly when $\\abs{f}^p$ has a harmonic majorant.\nWhen a harmonic majorant exists, there is a smallest one, the [[least harmonic majorant|G0H97JZRS9]].\n\n## Explanations\n\n### L1 human\n\nPicture the graph of a subharmonic function as a sagging sheet.\nA harmonic majorant is a tight, perfectly balanced sheet stretched above it that never dips below it.\nOn the unit disc, the constant $1$ is a harmonic majorant of $\\abs{z}^2$.\nOn the whole plane, $\\abs{z}^2$ has no harmonic majorant at all, because it grows too fast.\n",
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