Characterizations of nuclear pseudo-differential operators on S1 with applications to adjoints and products

Abstract

We give necessary and sufficient conditions on the symbols to guarantee that the corresponding pseudo-differential operators are nuclear from Lp1(S1) into Lp2(S1) for 1 ≤ p1, p2< ∞. Applications are given to adjoints of nuclear pseudo-differential operators from Lp2′(S1) into Lp1′(S1) for 1 ≤ p1, p2< ∞ and products of nuclear pseudo-differential operators on Lp(S1),1≤p<∞.