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On the hypoellipticity of convolution equations in the ultradistribution spaces of $ L\sp q$ growth


Author: Dušanka Kovačević
Journal: Proc. Amer. Math. Soc. 120 (1994), 1181-1190
MSC: Primary 46F10; Secondary 35H05, 44A35, 46F05
DOI: https://doi.org/10.1090/S0002-9939-1994-1197540-4
MathSciNet review: 1197540
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Abstract: We consider convolution equations in the ultradistribution spaces $ \mathcal{D}_{{L^q}}^{'({M_p})}$ and $ \mathcal{D}_{{L^q}}^{'\{ {M_p}\} },\;q \in [1,\infty ]$, of Beurling and Roumieu type of $ {L^q}$ growth. Our main aim is to find conditions for convolution operators to be hypoelliptic in $ \mathcal{D}_{{L^\infty }}^{'({M_p})}$ and $ \mathcal{D}_{{L^\infty }}^{'\{ {M_p}\} }$ respectively, in terms of their Fourier transforms.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1197540-4
Article copyright: © Copyright 1994 American Mathematical Society

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