Abstract
We study when sums of trigonometric series belong to given function classes. For this purpose we describe the Nikol’skii class of functions and, in particular, the generalized Lipschitz class. Results for series with positive and general monotone coefficients are presented.
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Dedicated to Academician S. M. Nikol’skii on the occasion of his 100th birthday
This work was partially supported by the Russian Foundation for Fundamental Research (grant no. 06-01-00268) and the Leading Scientific Schools (grant NSH-4681.2006.1). The author acknowledges financial support from the European Commission (Contract MIF1-CT-2004-509465). The paper was written while he was staying at the Centre de Recerca Matemática (CRM) in Barcelona, Spain.
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Tikhonov, S. Trigonometric series of Nikol’skii classes. Acta Math Hung 114, 61–78 (2007). https://doi.org/10.1007/s10474-006-0513-y
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DOI: https://doi.org/10.1007/s10474-006-0513-y