Boundedness of some pseudo-differential operators on generalized Triebel–Lizorkin spaces

Abstract

Let v : [0,∞) → ]0,∞) be a function such that the inequality v(ts) ≥ ct -μ v(s) holds for 0 < t,s ≤ 1 and some real number μ. In the generalized Triebel–Lizorkin spaces Fp,q v (R n ), we will study the boundedness of the pseudo-differential operators whose symbols belong to Hörmander´s class S 1,δ m ,0 ≤ δ < 1.