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On the convolution equations in the space of distributions of $ L\sp p$-growth


Author: D. H. Pahk
Journal: Proc. Amer. Math. Soc. 94 (1985), 81-86
MSC: Primary 46F10; Secondary 35H05, 46F05
DOI: https://doi.org/10.1090/S0002-9939-1985-0781061-9
MathSciNet review: 781061
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Abstract: We consider convolution equations in the space $ {D'_{{L^p}}},\;1 \leqslant p \leqslant \infty $, of distributions of $ {L^p}$-growth, i.e. distributions which are finite sums of derivatives of $ {L^p}$-functions (see [4, 7]). Our main results are to find a condition for convolution operators to be hypoelliptic in $ {\mathcal{D}'_{{L^\infty }}}$ in terms of their Fourier transforms and to show that the same condition is working for the solvability of convolution operators in the tempered distribution space $ \mathcal{S}'$ and $ {\mathcal{D}'_{{L^p}}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0781061-9
Article copyright: © Copyright 1985 American Mathematical Society

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