Article
| Title: | Fredholmness of pseudo-differential operators with nonregular symbols (English) |
| Author: | Yoshitomi, Kazushi |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 941-954 |
| Summary lang: | English |
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| Category: | math |
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| 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). (English) |
| Keyword: | Fredholmness |
| Keyword: | pseudo-differential operator |
| Keyword: | nonregular symbol |
| MSC: | 35S05 |
| MSC: | 47A53 |
| MSC: | 47G30 |
| idZBL: | Zbl 07729547 |
| idMR: | MR4632867 |
| DOI: | 10.21136/CMJ.2023.0387-22 |
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| Date available: | 2023-08-11T14:30:02Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151784 |
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| Reference: | [1] Abels, H.: Pseudodifferential and Singular Integral Operators: An Introduction With Applications.de Gruyter Graduate Lectures. Walter de Gruyter, Berlin (2012). Zbl 1235.35001, MR 2884718, 10.1515/9783110250312 |
| Reference: | [2] Abels, H., Pfeuffer, C.: Fredholm property of non-smooth pseudodifferential operators.Math. Nachr. 293 (2020), 822-846. Zbl 07206433, MR 4100541, 10.1002/mana.201800361 |
| Reference: | [3] Hörmander, L.: The Analysis of Linear Partial Differential Operators. III. Pseudo-Diffe-rential Operators.Grundlehren der Mathematischen Wissenschaften 274. Springer, Berlin (1994). Zbl 0601.35001, MR 1313500, 10.1007/978-3-540-49938-1 |
| Reference: | [4] Kohn, J. J., Nirenberg, L.: An algebra of pseudo-differential operators.Commun. Pure Appl. Math. 18 (1965), 269-305. Zbl 0171.35101, MR 0176362, 10.1002/cpa.3160180121 |
| Reference: | [5] Kumano-go, H.: Pseudo-Differential Operators.MIT Press, Cambridge (1982). Zbl 0489.35003, MR 0666870 |
| Reference: | [6] Nagase, M.: The $L^p$-boundedness of pseudo-differential operators with non-regular symbols.Commun. Partial Differ. Equations 2 (1977), 1045-1061. Zbl 0397.35071, MR 0470758, 10.1080/03605307708820054 |
| Reference: | [7] Taylor, M. E.: Pseudodifferential Operators and Nonlinear PDE.Progress in Mathematics 100. Brikhäuser, Boston (1991). Zbl 0746.35062, MR 1121019, 10.1007/978-1-4612-0431-2 |
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