Local solvability for a class of linear operators in Besov and Hölder spaces

We show local solvability in Besov 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 L∞(R,B∞,∞s(R)), B∞,∞s(R2) and Lq(R,Bp,qs(R)), 10 and not an integer (Hölder space), then we have local solvability for L in L∞(R,Cs(R)) and Cs(R2).