In this paper, we establish an analytic version of critical spaces $Q_{alpha}^{beta}(mathbb{R}^{n})$ on unit disc $mathbb{D}$, denoted by $Q^{beta}_{p}(mathbb{D})$. Further we prove a relation between $Q^{beta}_{p}(mathbb{D})$ and Morrey spaces. By t
he boundedness of two integral operators, we give the multiplier spaces of $Q^{beta}_{p}(mathbb{D})$.
In this note, we study the boundedness of integral operators $I_{g}$ and $T_{g}$ on analytic Morrey spaces. Furthermore, the norm and essential norm of those operators are given.
