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  • monotonicity condition  (1)
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    Electronic Resource
    Electronic Resource
    On a theorem of Marcinkiewicz and Zygmund (1998)
    Springer
    Mathematical notes 63 (1998), S. 338-341 
    Details
    ISSN: 1573-8876
    Keywords: Marcinkiewicz-Zygmund theorem ; monotonicity condition ; orthonormal system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let {ϕn(x)} be an orthonormal system on the closed interval [0,1], and let ∥ϕ n ∥∞ ≤M n . In 1937 Marcinkiewicz and Zygmund obtained an estimate of the norm inL q [0,1] of the sum of the series ∑ n=1 ∞ c n ϕ n (x) under the condition that {M n } is monotone increasing. In this paper it is shown that this condition cannot be discarded.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02317779
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