Geodesic
On a problem of Zygmund
Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 749-762

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It is proved that there exists an integrable function on $[0,1]^2$ whose integral is nondifferentiable in each direction belonging to a set everywhere dense in $[0,2\pi]$ but is strongly differentiable. 
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     author = {A. M. Stokolos},
     title = {On a problem of {Zygmund}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {749--762},
     publisher = {mathdoc},
     volume = {64},
     number = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a11/}
}
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A. M. Stokolos. On a problem of Zygmund. Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 749-762. http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a11/