Dirichlet-Morrey type spaces and Volterra integral operators

Abstract

A family of Dirichlet-Morrey type space D p,λ p−1 is introduced in this paper. For any positive Borel measure μ , the boundedness and compactness of the identity operator Id from D p,λ p−1 to tent spaces T p s (μ) are studied. As an application, the boundedness of the Volttera integral operators Tg and Ig, and the multiplication operator Mg from D p,λ p−1 to the general function space F(p, p− 1−λ ,s) are studied. The essential norm of Tg and Ig are also investigated.