Abstract
We begin by proving the equivalence between a \(2\pi \)-periodic function f belonging to the Nikol’skii space \(H^\alpha _2(-\pi ,\pi )\) for some \(0<\alpha < 1\) in the sense of Definition and the \(L^2\) Hölder condition of order \(\alpha \), i.e.,
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Serov, V. (2017). Absolute Convergence. Bernstein and Peetre Theorems.. In: Fourier Series, Fourier Transform and Their Applications to Mathematical Physics. Applied Mathematical Sciences, vol 197. Springer, Cham. https://doi.org/10.1007/978-3-319-65262-7_9
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DOI: https://doi.org/10.1007/978-3-319-65262-7_9
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-65261-0
Online ISBN: 978-3-319-65262-7
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