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Keywords:
Fredholmness; pseudo-differential operator; nonregular symbol
Summary:
We establish the Fredholmness of a pseudo-differential operator whose symbol is of class $C^{0,\sigma }$, $0<\sigma <1$, in the spatial variable. Our work here refines the work of H. Abels, C. Pfeuffer (2020).
References:
[1] Abels, H.: Pseudodifferential and Singular Integral Operators: An Introduction With Applications. de Gruyter Graduate Lectures. Walter de Gruyter, Berlin (2012). DOI 10.1515/9783110250312 | MR 2884718 | Zbl 1235.35001
[2] Abels, H., Pfeuffer, C.: Fredholm property of non-smooth pseudodifferential operators. Math. Nachr. 293 (2020), 822-846. DOI 10.1002/mana.201800361 | MR 4100541 | Zbl 07206433
[3] Hörmander, L.: The Analysis of Linear Partial Differential Operators. III. Pseudo-Diffe-rential Operators. Grundlehren der Mathematischen Wissenschaften 274. Springer, Berlin (1994). DOI 10.1007/978-3-540-49938-1 | MR 1313500 | Zbl 0601.35001
[4] Kohn, J. J., Nirenberg, L.: An algebra of pseudo-differential operators. Commun. Pure Appl. Math. 18 (1965), 269-305. DOI 10.1002/cpa.3160180121 | MR 0176362 | Zbl 0171.35101
[5] Kumano-go, H.: Pseudo-Differential Operators. MIT Press, Cambridge (1982). MR 0666870 | Zbl 0489.35003
[6] Nagase, M.: The $L^p$-boundedness of pseudo-differential operators with non-regular symbols. Commun. Partial Differ. Equations 2 (1977), 1045-1061. DOI 10.1080/03605307708820054 | MR 0470758 | Zbl 0397.35071
[7] Taylor, M. E.: Pseudodifferential Operators and Nonlinear PDE. Progress in Mathematics 100. Brikhäuser, Boston (1991). DOI 10.1007/978-1-4612-0431-2 | MR 1121019 | Zbl 0746.35062
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