Regularity criteria of almost every function in a Sobolev space

Aurélia Fraysse 1
1 Division Signaux - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : In this paper we determine the multifractal nature of almost every function (in the prevalence setting) in a given Sobolev or Besov space according to different regularity exponents. These regularity criteria are based on local $L^p$ regularity or on wavelet coefficients and give a precise information on pointwise behavior.
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Aurélia Fraysse. Regularity criteria of almost every function in a Sobolev space. Journal of Functional Analysis, Elsevier, 2010, pp.1806-1821. ⟨10.1016/j.jfa.2009.11.017⟩. ⟨hal-00555299v2⟩

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