On a class of almost hypoelliptic operators in generalized Sobolev spaces

The paper considers differential operators in the generalized Sobolev spaces. Differring necessary and sufficient conditions on the polyhedron ? are found, under which the function h _? ^s satisfies the Beurling condition for s great enough. They coincide (become necessary and sufficient) for polyhedrons in ? ₊ ² . The regularity of a class of differential equations is investigated.