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A family of functions with two different spectra of singularities

Abstract : Our goal is to study the multifractal properties of functions of a given family which have few non vanishing wavelet coefficients. We compute at each point the pointwise Holder exponent of these functions and also their local Lp regularity, computing the so-called p-exponent. We prove that in the general case the Holder and p exponent are different at each point. We also compute the dimension of the sets where the functions have a given pointwise regularity and prove that these functions are multifractal both from the point of view of Holder and Lp local regularity with different spectra of singularities. Furthermore, we check that multifractal formalism type formulas hold for functions in that family.
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Claire Coiffard Marre, Clothilde Melot, Thomas Willer. A family of functions with two different spectra of singularities. Journal of Fourier Analysis and Applications, Springer Verlag, 2014, 20 (5), pp.961-984. ⟨10.1007/s00041-014-9341-6⟩. ⟨hal-00831404v5⟩

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