Geodesic
On local behaviour of multi-dimensional harmonic variation
Izvestiya. Mathematics , Tome 70 (2006) no. 4, pp. 641-660

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In this paper, we study the behaviour of harmonic variation in a neighbourhood of a regular point for functions belonging to some multi-dimensional Waterman classes. As a consequence, some new results are obtained on the convergence of multiple trigonometric Fourier series for functions in these classes.
Keywords: Local extremal problems for bounded analytic nonvanishing functions; multiple Fourier series. 
@article{IM2_2006_70_4_a0,
     author = {A. N. Bakhvalov},
     title = {On local behaviour of multi-dimensional harmonic variation},
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     number = {4},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_4_a0/}
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A. N. Bakhvalov. On local behaviour of multi-dimensional harmonic variation. Izvestiya. Mathematics , Tome 70 (2006) no. 4, pp. 641-660. http://geodesic.mathdoc.fr/item/IM2_2006_70_4_a0/