Ck-Estimates for ∂¯-Equation on Certain Convex Domains of Infinite Type in Cn

In this paper, C k -estimates are obtained for the Henkin solution operator of the Cauchy–Riemann system ∂ ¯ u = φ on a class of certain smoothly bounded, convex domains of infinite type in C n , where φ is a ∂ ¯ -closed (0,  q )-differential form. It is proved that the Henkin solution of the ∂ ¯ -e...

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Bibliographic Details
Published in:The Journal of geometric analysis 2021, Vol.31 (2), p.2058-2087
Main Author: Ha, Ly Kim
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Domains
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
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Summary:In this paper, C k -estimates are obtained for the Henkin solution operator of the Cauchy–Riemann system ∂ ¯ u = φ on a class of certain smoothly bounded, convex domains of infinite type in C n , where φ is a ∂ ¯ -closed (0,  q )-differential form. It is proved that the Henkin solution of the ∂ ¯ -equation admits a suitable Hölder gain.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-019-00332-x