Jordan left derivations at the idempotent elements on reflexive algebras

We found several characterizations for the boundedness of the differences of integral-type operators from weighted Bergman spaces to $\beta$-Bloch—Orlicz spaces on the unit disk. In particular, their descriptions in terms of the $n$-th power of the induced analytic self-maps were also found. After that we estimated their essential norms, which can provide new compactness criteria. Finally, we completed this paper with analogous results for the differences of relevant integral-type operators acting from weighted Bergman spaces to $\beta$-Bloch—Orlicz spaces, which extend and strengthen several existing results in the literature.