scholarly journals HÖLDER ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS

2011 ◽  
Vol 48 (2) ◽  
pp. 241-252
Author(s):  
Sang-Hyun Cho
Keyword(s):  
Riemann Equation ◽  
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.

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