G. VARTANIAN ON LIMIT'S THEOREM FOR CLASS $H^1$ (7K, LATeX) ABSTRACT. In a recent paper by P.W.Jones and J.Journ\'e ({\it On weak convergence in $H^{1}(R^{d})$ }, Proc. Amer. Math. Soc. 120 (1994) , 137 - 138. ) , there are some inaccuracies. In this note, we give a counterexample to his theorem and a corrected form of the limit's theorem.