Geodesic
A~priori estimates and the Fredholm property for a~class of pseudo\-differential operators
Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 191-206

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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. 
@article{SM_1973_21_2_a1,
     author = {V. S. Rabinovich},
     title = {A~priori estimates and the {Fredholm} property for a~class of pseudo\-differential operators},
     journal = {Sbornik. Mathematics},
     pages = {191--206},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_2_a1/}
}
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V. S. Rabinovich. A~priori estimates and the Fredholm property for a~class of pseudo\-differential operators. Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 191-206. http://geodesic.mathdoc.fr/item/SM_1973_21_2_a1/