Equivalence of estimates on domain and its boundary

Authors

Tran Vu Khanh, University of WollongongFollow

RIS ID

105795

Publication Details

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

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).