Abstract
We give a condition under which a pseudodifferential operator with symbol in \(S^{m}\left (\mathbb {R}^{n}\times \mathbb {R}^{n}\right )\) cannot be a Fredholm operator when acting on suitable Besov and Triebel-Lizorkin spaces. As a corollary, we show that, if a classical pseudodifferential operator on \(\mathbb {R}^{n}\) is Fredholm in one of these spaces, then this operator must be elliptic.
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Acknowledgements
Pedro T. P. Lopes was partially supported by FAPESP (Processo n: 2016/07016-8).
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Lopes, P.T.P. (2019). Fredholmness and Ellipticity of ΨDOs on \(B_{pq}^{s}\left (\mathbb {R}^{n}\right )\) and \(F_{pq}^{s}\left (\mathbb {R}^{n}\right )\) . In: Molahajloo, S., Wong, M. (eds) Analysis of Pseudo-Differential Operators. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05168-6_3
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DOI: https://doi.org/10.1007/978-3-030-05168-6_3
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