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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Veröffentlicht in:The Journal of geometric analysis Jg. 26; H. 1; S. 287 - 293
1. Verfasser: Haslinger, Friedrich
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.01.2016
Schlagworte:
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
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Zusammenfassung: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