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Global Real Analyticity of the Kohn–Laplacian on Pseudoconvex CR Manifolds with Comparable Levi Form

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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

$$\begin{aligned} \Box _bu=f. \end{aligned}$$

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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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Science, Vietnam National University HoChiMinh City (VNU-HCM), 227 Nguyen Van Cu street, District 5, Ho Chi Minh City, Vietnam

    Ly Kim Ha

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  1. Ly Kim Ha
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Correspondence to Ly Kim Ha.

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Funding

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

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