sobolev estimates
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scholarly journals Uniform Sobolev estimates on compact manifolds involving singular potentials

2021 ◽  
Author(s):  
Matthew Blair ◽  
Xiaoqi Huang ◽  
Yannick Sire ◽  
Christopher Sogge
Keyword(s):  
Compact Manifolds ◽  
Singular Potentials ◽  
Sobolev Estimates

The complex green operator with Sobolev estimates up to a finite order

2020 ◽  
pp. 2050122
Author(s):  
Bingyuan Liu ◽  
Andrew Raich
Keyword(s):  
Sobolev Space ◽  
Finite Order ◽  
Green Operator ◽  
Cr Manifold ◽  
Regularity Properties ◽  
Sobolev Estimates ◽  
Higher Regularity

The purpose of this paper is to explore the geometry of a smooth CR manifold of hypersurface type and its relationship to the higher regularity properties of the complex Green operator on [Formula: see text]-forms in the [Formula: see text]-Sobolev space [Formula: see text] for a fixed [Formula: see text] and [Formula: see text].

The ∂¯-Neumann operator with Sobolev estimates up to a finite order

2020 ◽  
Vol 45 (10) ◽  
pp. 1435-1450
Author(s):  
Phillip Harrington ◽  
Bingyuan Liu
Keyword(s):  
Finite Order ◽  
Neumann Operator ◽  
Sobolev Estimates
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