Notes on commutators and Morrey spaces

Abstract

We show that the commutator [M_{b}, I_{\alpha}] of the multiplication operator M_{b} by b and the fractional integral operator I_{\alpha} is bounded from the Morrey space L^{p,\lambda}(R^{7\iota}) 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-\lambda) if and only if b belongs to BMO(Rn) .

Locations

• Hokkaido Mathematical Journal - View - PDF