Volterra integral operator on Dirichlet-Morrey type spaces

In this paper, we study the closed range property and the strict singularity of the Volterra integral operator Tg with the symbol g on Dirichlet-Morrey type spaces Dp−1p,K. Under some mild conditions, we show that Tg has no closed rang on Dp−1p,K and Tg is not strict singularity on Dp−1p,K.