Geodesic
The problem of boundary correspondence
Matematičeskie zametki, Tome 22 (1977) no. 1, pp. 103-108

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It is proved that those points of the boundary of the disk, to which a homeomorphism of the class $BL^{p,\alpha}$ cannot be extended according to Carathéodory (from the disk), form a set of zero $(p-\alpha)$–capacity. Estimates for the distortion of distances under these mappings are given. 
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     author = {B. P. Kufarev and V. M. Zyuz'kov},
     title = {The problem of boundary correspondence},
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B. P. Kufarev; V. M. Zyuz'kov. The problem of boundary correspondence. Matematičeskie zametki, Tome 22 (1977) no. 1, pp. 103-108. http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a10/