Sobolev Inequalities and the ∂¯-Neumann Operator

We study a complex-valued version of the Sobolev inequalities and its relationship to compactness of the ∂ ¯ -Neumann operator. For this purpose we use an abstract characterization of compactness derived from a general description of precompact subsets in L 2 -spaces. Finally we remark that the ∂ ¯...

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Bibliographic Details
Published in:	The Journal of geometric analysis Vol. 26; no. 1; pp. 287 - 293
Main Author:	Haslinger, Friedrich
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.01.2016
Subjects:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Primary 32W05 Neumann problem 35P10 Secondary 30H20 Compactness Sobolev inequalities
ISSN:	1050-6926, 1559-002X
Online Access:	Get full text
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Summary:	We study a complex-valued version of the Sobolev inequalities and its relationship to compactness of the ∂ ¯ -Neumann operator. For this purpose we use an abstract characterization of compactness derived from a general description of precompact subsets in L 2 -spaces. Finally we remark that the ∂ ¯ -Neumann operator can be continuously extended provided a subelliptic estimate holds.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-014-9549-3