Electronic Journal of Differential Equations, Vol. 2007(2007), No. 17, pp. 1-8. Title: Weighted function spaces of fractional derivatives for vector fields Author: Andras Domokos (California State Univ., Sacramento, Ca, USA) Abstract: We introduce and study weighted function spaces for vector fields from the point of view of the regularity theory for quasilinear subelliptic PDEs. Submitted May 26, 2006. Published January 25, 2007. Math Subject Classifications: 26A33, 35H20. Key Words: Fractional derivatives; weak solutions; subelliptic PDE.