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We prove that solutions for∂ get 1/M-derivatives more than the data in L p -Sobolev spaces on a bounded convex domain of finite type M by means of the integral kernel method. Also we prove that the Bergman projection is invariant under the L p -Sobolev spaces of fractional orders by different methods from McNeal-Stein's. By using these results, we can get L p -Sobolev estimates of order 1/M for the canonical solution for∂.

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