Characterization of Non-Smooth Pseudodifferential Operators

Spectral Invariance of Non-Smooth Pseudodifferential Operators

“…On account of the following lemma, cf. Lemma 3.5 in [2], we can prove similar boundedness results for non-smooth pseudodifferential operators. Lemma 3.13.…”

“…In the same manner as in the proof of Lemma 4.9 of [2] the previous result enables us to prove the next lemma:…”

“…if we split the supremum of the left side in the supremum over |x − y| > 1 and the rest. Using inequality (2) and…”

“…There are also boundedness results for non-smooth pseudodifferential operators, cf. Lemma 3.4 in [2], Theorem 3.7 in [2], Theorem 2.1 in [13], Lemma 2.9 in [13]: Lemma 3.9. Let 1 < q < ∞, m ∈ N 0 with m > n/q and τ > 0.…”

“…In the case M = ∞ we write A m ρ,0 ( m, q) instead of A m,∞ ρ,0 ( m, q). In [2] we showed that every operator in such a characterization set is a non-smooth pseudodifferential operator if certain conditions hold: Theorem 1.2. Let m ∈ R, 1 < q < ∞ and m ∈ N 0 with m > n/q.…”