The Comparison Test—Not Just for Nonnegative Series

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We consider the Dirichlet series ∞ ∑ k=2 akk −1−x =: f(x), x > 0, with coefficients ak ≥ 0 for all k. Among others, we prove exact estimates of certain weighted Lp-norms of f on the unit interval (0, 1) for any 0 < p <∞, in terms of the coefficients ak . Our estimation is based on the close relationship between Dirichlet series and power series. This enables us to derive exact estimates for int...

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ژورنال

عنوان ژورنال: Mathematics Magazine

سال: 2006

ISSN: 0025-570X,1930-0980

DOI: 10.1080/0025570x.2006.11953404