| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2023-08-11T14:30:02Z |
| Last updated:
|
2025-10-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151784 |
| . |
| 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 |
| . |
