Abstract
Relations between ω r(f,t) B and ω r+1(f,t) B of the sharp Marchaud and sharp lower estimate-type are shown to be satisfied for some Banach spaces of functions that are not rearrangement invariant. Corresponding results relating the rate of best approximation with ω r(f,t) B for those spaces are also given.
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Ditzian, Z. Rearrangement invariance and relations among measures of smoothness. Acta Math Hung 135, 270–285 (2012). https://doi.org/10.1007/s10474-011-0171-6
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DOI: https://doi.org/10.1007/s10474-011-0171-6