Abstract
In this paper, we study the global analytic hypoellipticity of the \(\Box _b\) operator on a general CR manifold of real dimension \((2n-1)\), with \(n\ge 3\). In particular, if M is a compact, real analytic, pseudoconvex CR manifold satisfying the \(D^{\epsilon }(q)\) and \((CR-P_q)\) conditions, and a special property for vector field T, we consider the following nonelliptic partial differential equation
If f is globally real analytic, we conclude that u is globally real analytic as well. The methods applied in this work are inspired from Tartakoff (1(4):283–311, 1976) and Tartakoff (89–90:85–116 1981).
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Acknowledgments
The author would like to thank Tran Vu Khanh for fruitful discussions to complete this work. The author is grateful to the referees for helpful comments to improve this paper.
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This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number C2016-18-17.
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Communicated by Jurgen Leiterer.
This paper is dedicated to the memory of Professor Giuseppe Zampieri.
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Ha, L.K. Global Real Analyticity of the Kohn–Laplacian on Pseudoconvex CR Manifolds with Comparable Levi Form. Complex Anal. Oper. Theory 11, 1329–1350 (2017). https://doi.org/10.1007/s11785-016-0570-3
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DOI: https://doi.org/10.1007/s11785-016-0570-3
Keywords
- CR-manifolds
- \(\Box _b\)-operator
- Real analyticity
- \(D^{\epsilon }(q)\)-condition
- \((CR-P_q)\)-condition
- Compactness estimates