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Proceedings of the American Mathematical Society

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The growth of hypoelliptic polynomials and Gevrey classes

Authors: E. Newberger and Z. Zieleźny
Journal: Proc. Amer. Math. Soc. 39 (1973), 547-552
MSC: Primary 35H05; Secondary 46E35
MathSciNet review: 0318660
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Abstract: For given hypoelliptic polynomials $ P$ and $ Q$, classes $ \Gamma _P^\rho (\Omega )$ and $ \Gamma _Q^\rho (\Omega )$ involving Gevrey type estimates on the successive iterates of the corresponding differential operators are defined. The equivalence of the inequality $ \vert Q(\xi ){\vert^2} \leqq C{(1 + \vert P(\xi ){\vert^2})^h},\xi \in {R^n}$, and the inclusion $ \Gamma _P^\rho (\Omega ) \subset \Gamma _Q^{\rho h}(\Omega )$ is proved.

References [Enhancements On Off] (What's this?)

  • [1] Lars Hörmander, Linear partial differential operators, Third revised printing. Die Grundlehren der mathematischen Wissenschaften, Band 116, Springer-Verlag New York Inc., New York, 1969. MR 0248435
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Keywords: Elliptic differential operator, hypoelliptic polynomial, Gevrey class
Article copyright: © Copyright 1973 American Mathematical Society