CHARPENTIER, Philippe; DUPAIN, Yves; MOUNKAILA, , Modi

doi:10.1090/proc/12660

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CHARPENTIER, Philippe
Institut de Mathématiques de Bordeaux [IMB]

DUPAIN, Yves
Institut de Mathématiques de Bordeaux [IMB]

MOUNKAILA, , Modi
Chercheur indépendant

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Proceedings of the American Mathematical Society. 2015-12, vol. 143, n° 12, p. 5337-5352

American Mathematical Society

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In this note we show that the weighted $L^{2}$-Sobolev estimates obtained by P. Charpentier, Y. Dupain \& M. Mounkaila for the weighted Bergman projection of the Hilbert space $L^{2}\left(\Omega,d\mu_{0}\right)$ where $\Omega$ is a smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^{n}$ and $\mu_{0}=\left(-\rho_{0}\right)^{r}d\lambda$, $\lambda$ being the Lebesgue measure, $r\in\mathbb{Q}_{+}$ and $\rho_{0}$ a special defining function of $\Omega$, are still valid for the Bergman projection of $L^{2}\left(\Omega,d\mu\right)$ where $\mu=\left(-\rho\right)^{r}d\lambda$, $\rho$ being any defining function of $\Omega$. In fact a stronger directional Sobolev estimate is established. Moreover similar generalizations are obtained for weighted $L^{p}$-Sobolev and lipschitz estimates in the case of pseudoconvex domain of finite type in $\mathbb{C}^{2}$ and for some convex domains of finite type.< Leer menos

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pseudo-convex

finite type

Levi form locally diagonalizable

convex

weighted Bergman projection

$\overline{\partial}_{\varphi}$-Neumann problem}

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On estimates for weighted Bergman projections

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