Constructive Description of Hardy–Sobolev Spaces on Strictly Pseudoconvex Domains

2022 ◽  
Vol 32 (2) ◽  
Author(s):  
Aleksandr Rotkevich
Keyword(s):  
Sobolev Spaces ◽  
Pseudoconvex Domains ◽  
Constructive Description

scholarly journals L2-Sobolev theory for the complex Green operator

2017 ◽  
Vol 28 (09) ◽  
pp. 1740006 ◽  
Author(s):  
Séverine Biard ◽  
Emil J. Straube
Keyword(s):  
Sobolev Spaces ◽  
Pseudoconvex Domains ◽  
Green Operator ◽  
Cr Geometry ◽  
Basic Formula ◽  
Cauchy Riemann ◽  
Cr Submanifolds

These notes are concerned with the [Formula: see text]-Sobolev theory of the complex Green operator on pseudoconvex, oriented, bounded and closed Cauchy–Riemann (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).

Sobolev Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Sobolev Spaces ◽  
Embedding Theorems ◽  
Approximation Numbers ◽  
Selection Of

This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.

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