Geodesic
The converse of the Fatou theorem for smooth measures
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 90-95

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We prove the converse of the Fatou theorem for small Zygmund measures defined on the Euclidean space. 
@article{ZNSL_2004_315_a5,
     author = {E. Doubtsov},
     title = {The converse of the {Fatou} theorem for smooth measures},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {90--95},
     publisher = {mathdoc},
     volume = {315},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a5/}
}
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E. Doubtsov. The converse of the Fatou theorem for smooth measures. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 90-95. http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a5/