J. Korean Math. Soc. 1998; 35(4): 981-997
Printed December 1, 1998
Copyright © The Korean Mathematical Society.
Tadato Matsuzawa
Meijo University
We shall show first general M\'etivier operators $D_y^2 + (x^{2l}+y^{2k})D_x^2, \ l,k = 1,2,\cdots$, have $G^{\{\theta,d\}}_{x,y}$-hypoellipticity in the vicinity of the origin $(0,0)$, where $\theta = \frac{l(1+k)} {l(1+k)-k}, d = \frac{\theta +k}{1+k}\ (>1)$, and finally the optimality of these exponents $\{\theta,d\}$ will be shown.
Keywords: Gevrey hypoellipticity, non-isotropic Gevrey exponents
MSC numbers: 34, 35, 46
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