Geodesic
On~the symbols of degenerate elliptic differential and hypoelliptic pseudodifferential operators
Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 543-561

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The author presents a general method of reducing the study of various degenerate operators to that of model operators with quasihomogeneous symbols whose hypoellipticity conditions are formulated in terms of an auxiliary operator-valued symbol. A set of symbols is constructed whose invertibility implies hypoellipticity. Bibliography: 13 titles. 
@article{IM2_1989_32_3_a4,
     author = {S. Z. Levendorskii},
     title = {On~the symbols of degenerate elliptic differential and hypoelliptic pseudodifferential operators},
     journal = {Izvestiya. Mathematics },
     pages = {543--561},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a4/}
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S. Z. Levendorskii. On~the symbols of degenerate elliptic differential and hypoelliptic pseudodifferential operators. Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 543-561. http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a4/