On the rate of pointwise divergence of Fourier and wavelet series in Lp

  • Authors:

  • Jean-Marie Aubry

  • Affiliations:

  • Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris XII Val-de-Marne, Créteil Cedex, France

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2006

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Abstract

Let g ∈ Lp (T), l p Sng(x) diverge as fast as nβ has Hausdorff dimension less or equal to 1 - βp. A comparable result holds for wavelet series. Conversely, we show that this inequality is sharp and depends only on the Hausdorff dimension of the set of divergence.