Differences of products of composition operator and integral type operator on α-Bloch-Orlicz space

Abstract:

In this paper, we study the difference of the products of composition operator and integral type operator $C_\varphi I_g$ and $I_gC_\varphi$ acting on the $\alpha$-Bloch-Orlicz space $\mathcal{B}_\alpha^\phi$ in the unit disk. By constructing different test functions, we present some necessary and sufficient conditions for the boundedness and compactness of the difference.