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Equivalence of estimates on domain and its boundary

Journal Article


Abstract


  • Let Ω be a pseudoconvex domain in Cn with smooth boundary bΩ. We define general estimates (f-M)kΩ and (f-M)kbΩ on k-forms for the complex Laplacian □ on Ω and the Kohn–Laplacian □ b on bΩ. For 1 ≤ k ≤ n−2, we show that (f-M) kbΩ holds if and only if (f-M) kΩ and (f-M)n−k−1Ωhold. Our proof relies on Kohn’s method in Kohn (Ann. Math.156(2), 213–248, 2002).

Publication Date


  • 2016

Citation


  • Khanh, T. (2016). Equivalence of estimates on domain and its boundary. Vietnam Journal of Mathematics, 44 (1), 29-48.

Scopus Eid


  • 2-s2.0-84960889150

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5451

Number Of Pages


  • 19

Start Page


  • 29

End Page


  • 48

Volume


  • 44

Issue


  • 1

Place Of Publication


  • http://link.springer.com/article/10.1007/s10013-015-0160-0

Abstract


  • Let Ω be a pseudoconvex domain in Cn with smooth boundary bΩ. We define general estimates (f-M)kΩ and (f-M)kbΩ on k-forms for the complex Laplacian □ on Ω and the Kohn–Laplacian □ b on bΩ. For 1 ≤ k ≤ n−2, we show that (f-M) kbΩ holds if and only if (f-M) kΩ and (f-M)n−k−1Ωhold. Our proof relies on Kohn’s method in Kohn (Ann. Math.156(2), 213–248, 2002).

Publication Date


  • 2016

Citation


  • Khanh, T. (2016). Equivalence of estimates on domain and its boundary. Vietnam Journal of Mathematics, 44 (1), 29-48.

Scopus Eid


  • 2-s2.0-84960889150

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5451

Number Of Pages


  • 19

Start Page


  • 29

End Page


  • 48

Volume


  • 44

Issue


  • 1

Place Of Publication


  • http://link.springer.com/article/10.1007/s10013-015-0160-0