... equations, Comm. PDE. 17 (19 92) 14 07 14 56. 12 . H. Triebel, Theory of Function space ,Birkh¨auser, Basel, 19 83. 13 . H. Triebel, Theory of Function space II, Birkh¨auser, Basel, 19 92. 14 . H. Triebel, ... (y)| (1 + 2j|x − y|)a Φ∗af(x)2−j(S +1) .So we obtainψ∗j,af(x) Φ∗af(x)2−j(S +1) +∞k =1 ϕ∗k,af(x) ×2(k−j)(S +1) if,k j,2(j−k)(S +1) if,k≥ j.Hence with δ =min (1, S +1 ... ×2(k−j)(S +1) if,k j,2(j−k)(S +1) if,k≥ j.Note that for k = 1, we do not use the condition Dτλ(0) = 0 in the above proof of the last estimate, so by replacing respectively λ 1 and ϕ 1 with Λ...