Local solvability for a class of linear operators in Triebel-Lizorkin spaces

Abstract

We show local solvability in Triebel-Lizorkin spaces for a class of first order linear operators L defined on an open set of Rn+1, n∈N, satisfying the condition (P) of Nirenberg-Treves and whose coefficients are Hölder continuous. Moreover, when n=1, we show local solvability for L, in Lp(R,h1(R)), 1<p≤∞, where F1,20=h1 (local Hardy space), local solvability for L in bmo(R2) where F∞,20=bmo(R2) (local bounded mean oscillation space) and local solvability for L in Lr(R,Fp,qs(R)), 1≤r≤∞, 1<p<q≤∞ and s∈R.