On solutions of almost hypoelliptic equations in weighted Sobolev spaces

It is proved that if P(D) is a regular, almost hypoelliptic operator and

$ L_{2,\delta } = \left\{ {u:\left\| u \right\|_{2,\delta } = \left {\int {\left( {|u(x)|e^{ - \delta |x|} } \right)^2 dx} } \right]^{1/2} < \infty } \right\},\delta > 0, $ L_{2,\delta } = \left\{ {u:\left\| u \right\|_{2,\delta } = \left {\int {\left( {|u(x)|e^{ - \delta |x|} } \right)^2 dx} } \right]^{1/2} < \infty } \right\},\delta > 0,
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