In this note, we mainly study Bergman-Morrey space. Firstly, we prove atomic decomposition of \(A^{p,\lambda }(\mathbb {D})\) . Secondly, we consider interpolation problem of \(A^{p,\lambda }(\mathbb {D})\) . Thirdly, we characterize the boundedness of the composition operator on \(A^{p,\lambda }(\mathbb {D})\) . Fourthly, we describe closed range composition operator and integral operator on Bergman-Morrey space. Fifthly, we show that \(A^{p,\lambda }(\mathbb {D})\) is a Banach algebra with respect to the Duhamel product. Finally, semigroups of composition operators and Jackson’s theorem in Bergman-Morrey space are investigated.
