Boundedness of variation, oscillation and maximal differential transform on BMO space

In this paper, we prove that the oscillation operator, variation operator and maximal differential transform associated with the approximate identities are bounded from $\mathrm{B}\mathrm{M}\mathrm{O}({\mathbb{R}}^n)$ to its subspace $\mathrm{B}\mathrm{L}\mathrm{O}({\mathbb{R}}^n)$.