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Abstract and Applied Analysis
Volume 2015, Article ID 731068, 6 pages
Research Article

On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in with One Degenerate Eigenvalue

1Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
2Department of Mathematics, Indiana University East, Richmond, IN 47374, USA

Received 8 October 2015; Accepted 5 November 2015

Academic Editor: Chun-Gang Zhu

Copyright © 2015 Sanghyun Cho and Young Hwan You. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let be a smoothly bounded pseudoconvex domain in with one degenerate eigenvalue and assume that there is a smooth holomorphic curve whose order of contact with at is larger than or equal to . We show that the maximal gain in Hölder regularity for solutions of the -equation is at most .