The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set W⊂R+n containing the intersection of some neighborhood of the origin with R+n. It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.
Oniani G.G., Tulone F. (2019). On the Almost Everywhere Convergence of Multiple Fourier-Haar Series. JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS, 54(5), 288-295 [10.3103/S1068362319050054].
On the Almost Everywhere Convergence of Multiple Fourier-Haar Series
Tulone F.
2019-01-01
Abstract
The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set W⊂R+n containing the intersection of some neighborhood of the origin with R+n. It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.
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