The Bergman projection and weighted 𝐶^{𝑘} estimates for the canonical solution to the ∂̄ problem on non-smooth domains

Ehsani, Dariush

doi:10.1090/S0002-9947-2011-05277-3

The Bergman projection and weighted $C^k$ estimates for the canonical solution to the $\bar {\partial }$ problem on non-smooth domains
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Trans. Amer. Math. Soc. 363 (2011), 3959-3975 Request permission

Abstract:

We apply integral representations for functions on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted $C^k$-estimates for the component of a given function, $f$, which is orthogonal to holomorphic functions in terms of $C^k$-norms of $\bar {\partial } f$. The weights are powers of the gradient of the defining function of the domain.

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