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Estimates for regularity of the tangential \documentclass{article}\usepackage{amssymb,amsmath}\begin{document}\pagestyle{empty}$\bar{\partial }$\end{document} ‐system
Author(s) -
Khanh Tran Vu,
Zampieri G.
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910279
Subject(s) - bar (unit) , hypersurface , mathematics , submanifold , combinatorics , mathematical analysis , physics , meteorology
We study ellipticity in a weak sense, such as fractional or logarithmic, of the system \documentclass{article}\usepackage{amssymb,amsmath}\begin{document}\pagestyle{empty}$\big (\bar{\partial }_b,\bar{\partial }^*_b\big )$\end{document} tangential to a hypersurface or a generic higher codimensional submanifold \documentclass{article}\usepackage{amssymb,amsmath}\begin{document}\pagestyle{empty}$M\subset {\mathbb {C}}^n$\end{document} . The geometric setting which assures the estimates is the q ‐pseudoconvexity/concavity of M in addition to the existence of a suitable family of weights in a strip or a tube around M . The basic estimates for the \documentclass{article}\usepackage{amssymb,amsmath}\begin{document}\pagestyle{empty}$\bar{\partial }$\end{document} ‐Neumann problem on q ‐pseudoconvex/concave domains is related to the classical work by Shaw 17 and more recent by Zampieri 19. The method of the weights is due to Catlin 3 and the relation between the tangential and the ambient \documentclass{article}\usepackage{amssymb,amsmath}\begin{document}\pagestyle{empty}$\bar{\partial }$\end{document} system on pseudoconvex domains is inspired to Kohn 14. Both these techniques are adapted here to a general Levi signature.