Bounded Point Derivations and Functions of Bounded Mean Oscillation

Let X be a compact subset of the complex plane with property that every relatively open has positive area and let $$A_0(X)$$ denote space VMO functions are analytic on X. is said to admit bounded point derivation order t at $$x_0 \in \partial X$$ if there exists constant C such $$|f^{(t)}(x_0)|\le \Vert f\Vert _{{\text {BMO}}}$$ for all in $${\text {VMO}}(X)$$ In this paper, we give necessary sufficient conditions terms lower 1-dimensional Hausdorff content $$x_0$$ . These similar existence derivations other spaces.