Geodesic
A~multidimensional analog of a~theorem due to Zygmund
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 717-727

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Zygmund proved an inequality describing the dependence of the modulus of continuity of the adjoint function on that of the original function lying in the space of $2\pi$-periodic continuous functions. The present article contains estimates of partial moduli of continuity of the adjoint function of several variables in the space $C$. Examples show that these estimates are sharp. 
@article{MZM_1997_61_5_a8,
     author = {V. A. Okulov},
     title = {A~multidimensional analog of a~theorem due to {Zygmund}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {717--727},
     publisher = {mathdoc},
     volume = {61},
     number = {5},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a8/}
}
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V. A. Okulov. A~multidimensional analog of a~theorem due to Zygmund. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 717-727. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a8/