A distribution T in Ω is
said to be strongly regular with respect to the differential operator P(D), if
Pk(D)T,k = 0,1,⋯ , are of bounded order in any open set Ω′⊂⊂ Ω. Necessary and
sufficient conditions on the polynomials P and Q are established in order that a
distribution T strongly regular with respect to P(D) be strongly regular with respect
to Q(D).
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