On a class of maximally hypoelliptic operators

The maximal hypoellipticity of the operator X ₁ ^2m , ... X _k ^2m is proved, where X_j are first-order pseudodifferential operators and m is a natural number. It is assumed that the set of these operators and their first-order commutators is an elliptic system. The results obtained generalize the well-known results of Hormander, Oleinik, and Radkevich, Kohn, Helffer, and Nourrigat, and Rothshield and Stein. Bibliography: 9 titles. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 17, pp. 3–26, 1994.