What strong monotonicity condition on Fourier coefficients can make the ratio $\Vert f-S_ n(f)\Vert /E_ n(f)$ be bounded?
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- by S. P. Zhou
- Proc. Amer. Math. Soc. 121 (1994), 779-785
- DOI: https://doi.org/10.1090/S0002-9939-1994-1198461-3
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Abstract:
Let $\{ {\phi _n}\} _{n = 1}^\infty$ be a positive increasing sequence and ${\phi _n}\hat f(n)$ decrease. We ask what exact conditions on $\{ {\phi _n}\}$ make $\left \| {f - {S_n}(f)} \right \|/{E_n}(f)$ bounded? The present paper will give a complete answer to it.References
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- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 779-785
- MSC: Primary 42A10; Secondary 42A20, 42A32
- DOI: https://doi.org/10.1090/S0002-9939-1994-1198461-3
- MathSciNet review: 1198461