Right Type Departmental Bulletin Paper

Abstract of the Talk We show a factorization theorem on Hardy space $H^{1}(R^{n}) $ in terms of the fractional integral operator and both functions in classical Morrey space and functions generated by blocks. Consequently, we show that the commutator $[M_{b}, I_{\alpha}] $ of the multiplication operatorM & by $b $ and the fractional integral operator $I_{\alpha} $ is bounded from the Morrey space $L^{p,\lambda}(R^{n}) $ to the Morrey space $L^{q,\lambda}(R^{n}) $ where $1<p<\infty,0<\alpha<n,0<\lambda<n-\alpha p $ and $1/q=1/p-\alpha/(n- \mathrm{X}) $ if and only if $b $ belongs to $BMO(R^{n}) $.