L-2-Sobolev theory for the complex Green operator Academic Article

abstract

• These notes are concerned with the [Formula: see text]-Sobolev theory of the complex Green operator on pseudoconvex, oriented, bounded and closed CauchyRiemann (CR)-submanifolds of [Formula: see text] of hypersurface type. This class of submanifolds generalizes that of boundaries of pseudoconvex domains. We first discuss briefly the CR-geometry of general CR-submanifolds and then specialize to this class. Next, we review the basic [Formula: see text]-theory of the tangential CR operator and the associated complex Green operator(s) on these submanifolds. After these preparations, we discuss recent results on compactness and regularity in Sobolev spaces of the complex Green operator(s).

authors

• Straube, Emil

published proceedings

• INTERNATIONAL JOURNAL OF MATHEMATICS

author list (cited authors)

• Biard, S., & Straube, E. J.

citation count

• 7

complete list of authors

• Biard, Severine||Straube, Emil J

publication date

• August 2017

publisher

• World Scientific Publishing  Publisher

published in

• International Journal of Mathematics  Journal

keywords

• Closed Range
• Compactness
• Complex Green Operator
• Cr-submanifold Of Hypersurface Type
• Partial Derivative(m)
• Sobolev Estimates

Digital Object Identifier (DOI)

• 10.1142/S0129167X17400067

start page

• 1740006

end page

• 1740006

volume

• 28

issue

• 9

URL

• http://dx.doi.org/10.1142/s0129167x17400067