Abstract
Let Ω be a bounded convex domain in Cn, with smooth boundary of finite type m.
The equation $\bar \partial u = f$ is solved in Ω with sharp estimates: if f has bounded coefficients, the coefficients of our solution u are in the Lipschitz space Λ. Optimal estimates are also given when data have coefficients belonging to Lp(Ω), p≥1.
We solve the $\bar \partial $ -equation by means of integral operators whose kernels are not based on the choice of a “good” support function. Weighted kernels are used; in order to reflect the geometry of bΩ, we introduce a weight expressed in terms of the Bergman kernel of Ω.
Citation
Anne Cumenge. "Sharp estimates for $\bar \partial $ on convex domains of finite typeon convex domains of finite type." Ark. Mat. 39 (1) 1 - 25, March 2001. https://doi.org/10.1007/BF02388789
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