Geodesic
Boundary interpolation in the weak Lipschitz classes
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 36, Tome 355 (2008), pp. 72-80

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For the Lipschitz spaces with the weak modules of continuity $\omega_\alpha(t)=\exp(-\log^\alpha\frac1t)$, $0\alpha1$, conditions sufficient for interpolation are found that are very close to being necessary. Bibl. – 7 titles. 
@article{ZNSL_2008_355_a2,
     author = {A. V. Vasin},
     title = {Boundary interpolation in the weak {Lipschitz} classes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {72--80},
     publisher = {mathdoc},
     volume = {355},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_355_a2/}
}
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A. V. Vasin. Boundary interpolation in the weak Lipschitz classes. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 36, Tome 355 (2008), pp. 72-80. http://geodesic.mathdoc.fr/item/ZNSL_2008_355_a2/