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  "body": "\n## Summary\n\nThe Bergman projection of a domain $\\Omega \\subseteq \\C^n$ is the [[orthogonal projection|0B8KZRT28M]] of $L^2(\\Omega)$ onto its closed subspace of holomorphic functions, the [[Bergman space|2D619WTPYC]].\nIt is an integral operator whose kernel is the [[Bergman kernel|8RWDHW0CXC]].\nIts regularity, for example whether it maps smooth functions on the closure to smooth functions, governs the boundary behaviour of biholomorphic maps.\nIt is closely tied to the $\\bar\\partial$-Neumann problem, through Kohn's formula $P = I - \\bar\\partial^* N \\bar\\partial$.\n\n## Explanations\n\n### L1 human\n\nAmong all square-integrable functions on a domain, the holomorphic ones form a closed subspace.\nThe Bergman projection sends each function to the holomorphic function closest to it in the $L^2$ sense.\nIt does so by integrating the function against the Bergman kernel.\nFor example, on the unit disc it sends $\\bar z$ to $0$ and $z^k$ to itself.\n",
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