Geodesic
On peak sets for H\"older classes (a~counterexample to E.~M.~Dyn'kin's conjecture)
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 45-54

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We construct a peak set $E\subset\mathbb T$ for the analytic Hölder class $A_\alpha$ ($0\alpha1$) such that $\operatorname{dist}(\cdot,E)^{-\alpha}\notin L^1(\mathbb T)$. 
@article{ZNSL_1987_157_a3,
     author = {B. J\"oricke},
     title = {On peak sets for {H\"older} classes (a~counterexample to {E.~M.~Dyn'kin's} conjecture)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {45--54},
     publisher = {mathdoc},
     volume = {157},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a3/}
}
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B. Jöricke. On peak sets for H\"older classes (a~counterexample to E.~M.~Dyn'kin's conjecture). Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 45-54. http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a3/