On Solutions of Almost Hypoelliptic Equations in Weighted Sobolev Spaces

摘要

It is proved that if P(D) is a regular, almost hypoelliptic operator andrnL_(2,δ) = {u : ‖u‖_(2,δ) = [∫ (|u(x)|e~(-δ|x|))~2 dx]~(1/2)< ∞}, δ > 0,rnand H_δ~∞ is the e~(δ|x|)-weighted Sobolev space, then there exists a number δ_0 > 0 such that all solutions u ∈ L_(2,δ) of the differential equation P(D)u = f belong to H_δ~∞ for any f ∈ H_δ~∞ with some δ ≤ δ_0.