This is true.  See, for instance, Theorem 4.3.1 in ["Introduction to the Theory of Distributions"][1] by 
Friedlander and Joshi.


  [1]: http://books.google.co.uk/books?id=9O-pXIVUEFMC&printsec=frontcover&dq=Introduction+to+the+Theory+of+Distributions&hl=en&ei=vmhhTIimAZS7jAe9-OyvCQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA#v=onepage&q&f=false