On the divergence of Fourier series in the spaces ϕ(L) containing L
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The paper deals with the question of the divergence of Fourier series in function spaces wider than L = L[−π, π], but narrower than L p = L p [−π, π] for all p ∈ (0, 1). It is proved that the recent results of Filippov on the generalization to the space ϕ(L) of Kolmogorov’s theorem on the convergence of Fourier series in L p , p ∈ (0, 1), cannot be improved.
KeywordsFourier series the space ϕ(L) the spaces Lp p ∈ (0 1) convergence of Fourier series integrable function
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- 1.H. K. Bari, Trigonometric Series (Fizmatgiz, Moscow, 1961) [in Russian].Google Scholar