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Let $X$ be a compact subset of the complex plane and $x \in X$. A necessaryand sufficient condition is given in terms of Hausdorff contents for theexistence of a bounded point derivation at $x$ on the space of vanishingCampanato functions that are analytic in a neighborhood of $X$. Thisgeneralizes many known conditions for the existence of bounded pointderivations on other function spaces.

Bounded point derivations on Campanato spaces