On maximal Sobolev and Holder estimates for the tangential Cauchy-Riemann operator and boundary Laplacian

2002 ◽  
Vol 124 (1) ◽  
pp. 129-197 ◽  
Author(s):  
Kenneth Douglas Koenig
Keyword(s):  
Cauchy Riemann ◽  
Hölder Estimates

scholarly journals On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains inCnwith One Degenerate Eigenvalue

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Sanghyun Cho ◽  
Young Hwan You
Keyword(s):  
Pseudoconvex Domain ◽  
Pseudoconvex Domains ◽  
Hölder Regularity ◽  
Holomorphic Curve ◽  
Riemann Equation ◽  
Degenerate Eigenvalue ◽  
Cauchy Riemann ◽  
Maximal Gain ◽  
Holder Regularity ◽  
Hölder Estimates

LetΩbe a smoothly bounded pseudoconvex domain inCnwith one degenerate eigenvalue and assume that there is a smooth holomorphic curveVwhose order of contact withbΩatz0∈bΩis larger than or equal toη. We show that the maximal gain in Hölder regularity for solutions of the∂¯-equation is at most1/η.

scholarly journals On Symmetric Cauchy–Riemann Manifolds

2000 ◽  
Vol 149 (2) ◽  
pp. 145-181 ◽  
Author(s):  
Wilhelm Kaup ◽  
Dmitri Zaitsev
Keyword(s):  
Riemann Manifolds ◽  
Cauchy Riemann
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