Title

On a theorem of P. L. Uljanov

Abstract

It is shown that if c(n) = o(1), |n| → ∞, and ∑|n| < ∞|Δm c(n)| < ∞, for some integer m ≥ 1, then the series ∑|n| < ∞c(n)eint converges to some f ∈ I.p(T) for any 0 < p < 1/m.

Document Type

Article

DOI

https://doi.org/10.1090/S0002-9939-1984-0728350-0

Keywords

Convergence in L (T)-metric (0 < p < 1) of trigonometric series p

Publication Date

1-1-1984

Journal Title

Proceedings of the American Mathematical Society

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