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- W2606730000 abstract "We obtain sharp weighted estimates for solutions of the equation $$overline{partial }u=f$$ in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces $$L^{p}(Omega ,delta ^{gamma })$$ , $$delta $$ being the distance to the boundary, with two different types of hypothesis on the form f: first, if the data f belongs to $$L^{p}left( Omega ,delta _{Omega }^{gamma }right) $$ , $$gamma >-1$$ , we have a mixed gain on the index p and the exponent $$gamma $$ ; secondly we obtain a similar estimate when the data f satisfies an apropriate anisotropic $$L^{p}$$ estimate with weight $$delta _{Omega }^{gamma +1}$$ . Moreover we extend those results to $$gamma =-1$$ and obtain $$L^{p}(partial Omega )$$ and $$BMO(partial Omega )$$ estimates. These results allow us to extend the $$L^{p}(Omega ,delta ^{gamma })$$ -regularity results for weighted Bergman projection obtained in Charpentier et al. (Complex Var Elliptic Equ 59(8):1070–1095, 2014) for convex domains to more general weights." @default.
- W2606730000 created "2017-04-28" @default.
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- W2606730000 date "2017-12-09" @default.
- W2606730000 modified "2023-09-23" @default.
- W2606730000 title "Weighted and boundary $$L^{p}$$ L p estimates for solutions of the $$overline{partial }$$ ∂ ¯ -equation on lineally convex domains of finite type and applications" @default.
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- W2606730000 doi "https://doi.org/10.1007/s00209-017-2015-8" @default.
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