Abstract
A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a function belonging to all \({L^{p}}\) spaces, \({1\leq p < \infty}\). We obtain new results on strong convergence of Fourier series for functions of generalized bounded variation.
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To the memory of Naza Tanović-Miller
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Avdispahić, M., Šabanac, Z. Strong boundedness, strong convergence and generalized variation. Acta Math. Hungar. 152, 404–420 (2017). https://doi.org/10.1007/s10474-017-0717-3
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DOI: https://doi.org/10.1007/s10474-017-0717-3