Optimal Sobolev estimates for ¯∂ on convex domains of finite type

• Autores: H. Ahn, H. R. Cho
• Localización: Mathematische zeitschrift, ISSN 0025-5874, Vol. 243, Nº 4, 2003, pág. 837
• Idioma: inglés
• DOI: 10.1007/s00209-003-0525-z
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• Resumen

  • 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 ¯∂.