Abstract
In this work we study C ∞-hypoellipticity in spaces of ultradistributions for analytic linear partial differential operators. Our main tool is a new a-priori inequality, which is stated in terms of the behaviour of holomorphic functions on appropriate wedges. In particular, for sum of squares operators satisfying Hörmander’s condition, we thus obtain a new method for studying analytic hypoellipticity for such a class. We also show how this method can be explicitly applied by studying a model operator, which is constructed as a perturbation of the so-called Baouendi-Goulaouic operator.
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This research project was supported by the NSF Grant INT 0227100. The first author was also partially supported by CNPq and Fapesp.
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Cordaro, P.D., Hanges, N. Hypoellipticity in spaces of ultradistributions—Study of a model case. Isr. J. Math. 191, 771–789 (2012). https://doi.org/10.1007/s11856-012-0011-6
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DOI: https://doi.org/10.1007/s11856-012-0011-6