Geodesic
A priori estimates and the Fredholm property for a class of pseudo­differential operators
Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 191-206 Cet article a éte moissonné depuis la source Math-Net.Ru

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Pseudodifferential operators with symbols $A(x,\xi)$ satisfying \begin{equation} |D^\beta_xD_\xi^\alpha A(x,\xi)|\leqslant C^A_{\alpha,\beta}(1+|\xi'|)^{m'-|\alpha'|}(1+|\xi''|)^{m''-|\alpha''|} \end{equation} for all multi-indices $\alpha$, $\beta$, where $\xi=(\xi',\xi'')$ and $\alpha=(\alpha',\alpha'')$, are considered. For operators of this class a priori estimates (in part as well as all of the variables) are established. Necessary and sufficient conditions are found for some classes of pseudodifferential operators with symbols satisfying (1) to have the Fredholm property. Bibliography: 11 titles. 
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V. S. Rabinovich. A priori estimates and the Fredholm property for a class of pseudo­differential operators. Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 191-206. http://geodesic.mathdoc.fr/item/SM_1973_21_2_a1/

[1] L. Khermander, “Psevdodifferentsialnye operatory i gipoellipticheskie uravneniya”, Psevdodifferentsialnye operatory, izd-vo «Mir», Moskva, 1967, 297–367 | MR

[2] V. V. Grushin, “Ob odnom klasse gipoellipticheskikh operatorov”, Matem. sb., 83 (125) (1970), 456–473 | Zbl

[3] V. V. Grushin, “Ob odnom klasse ellipticheskikh psevdodifferentsialnykh operatorov, vyrozhdayuschikhsya na podmnogoobrazii”, Matem. sb., 84 (126) (1971), 163–195 | Zbl

[4] L. R. Volevich, “Lokalnye svoistva neodnorodnykh psevdodifferentsialnykh operatorov”, Trudy Mosk. matem. ob-va, X (1967), 52–98

[5] R. G. Douglas, R. Howe, “On the $C^*$-algebra of Toeplitz operators on the quarter-plane”, Trans. Amer. Math. Soc., 158 (1971), 203–218 | DOI | MR

[6] L. Schwartz, “Distributions a valeurs vectorielles. I; II”, Ann. Inst. Fourier, 7 (1957), 1–141 ; 8 (1958), 1–209 | MR | Zbl | Zbl

[7] V. V. Grushin, “Psevdodifferentsialnye operatory v $R^n$ s ogranichennymi simvolami”, Funkts. analiz, 4:3 (1970), 37–50 | MR | Zbl

[8] V. S. Rabinovich, “Psevdodifferentsialnye uravneniya v neogranichennykh oblastyakh”, DAN SSSR, 197:2 (1971), 284–287 | MR | Zbl

[9] V. S. Rabinovich, “Kvazielltspticheskie psevdodifferentsialnye operatory i zadacha Koshi dlya parabolicheskikh uravnenii”, DAN SSSR, 201:5 (1971), 1055–1058 | Zbl

[10] I. B. Simonenko, “Novyi obschii metod issledovaniya lineinykh operatornykh uravnenii tipa singulyarnykh integralnykh uravnenii, I”, Izv. AN SSSR, seriya matem., 29 (1965), 567–586 | MR | Zbl

[11] V. S. Pilidi, “O mnogomernykh bisingulyarnykh operatorakh”, DAN SSSR, 201:4 (1971), 787–789 | MR | Zbl