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On the rate of pointwise divergence of Fourier and wavelet series in L-p

Abstract : Let g is an element of L-p(T), 1 < p < infinity. We show that the set of points where the Fourier partial sums S(n)g(x) diverge as fast as n(beta) has Hausdorff dimension less or equal to 1 - beta p. 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. (c) 2005 Elsevier Inc. All rights reserved.
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Jean-Marie Aubry. On the rate of pointwise divergence of Fourier and wavelet series in L-p. Journal of Approximation Theory, Elsevier, 2006, 138 (1), pp.97--111. ⟨10.1016/j.jat.2005.10.003⟩. ⟨hal-00693104⟩

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