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Uniformly convergent Fourier series and multiplication of functions
V. V. Lebedev National Research University Higher School of Economics, ul. Tallinskaya 34, Moscow, 123458 Russia
Abstract:
Let $U(\mathbb T)$ be the space of all continuous functions on the circle $\mathbb T$ whose Fourier series converges uniformly. Salem's well-known example shows that a product of two functions in $U(\mathbb T)$ does not always belong to $U(\mathbb T)$ even if one of the factors belongs to the Wiener algebra $A(\mathbb T)$. In this paper we consider pointwise multipliers of the space $U(\mathbb T)$, i.e., the functions $m$ such that $mf\in U(\mathbb T)$ whenever $f\in U(\mathbb T)$. We present certain sufficient conditions for a function to be a multiplier and also obtain some Salem-type results.
Keywords:
uniformly convergent Fourier series, function spaces, multiplication operators.
Received: April 1, 2018
Citation:
V. V. Lebedev, “Uniformly convergent Fourier series and multiplication of functions”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 186–192; Proc. Steklov Inst. Math., 303 (2018), 171–177
Linking options:
https://www.mathnet.ru/eng/tm3946https://doi.org/10.1134/S0371968518040143 https://www.mathnet.ru/eng/tm/v303/p186
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Abstract page: | 360 | Full-text PDF : | 80 | References: | 45 | First page: | 20 |
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