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Proceedings of the American Mathematical Society

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A new $ \ell \sb{1}$ estimate and a problem of Katznelson


Author: D. J. Newman
Journal: Proc. Amer. Math. Soc. 31 (1972), 225-227
MSC: Primary 42A16
DOI: https://doi.org/10.1090/S0002-9939-1972-0296588-7
MathSciNet review: 0296588
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Abstract: We produce a new estimate on the $ {l_1}$ norm in terms of the closeness of approximation by functions with small derivatives. We thereby solve a problem of Katznelson and give new proofs of some old $ {l_1}$ estimates.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296588-7
Keywords: $ {l_1}$ norms, functional analysis fourier series
Article copyright: © Copyright 1972 American Mathematical Society

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