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We consider the smoothness parameter of a function f ∈ L²(ℝ) in terms of Besov spaces $B_{2,\infty }^s\left(ℝ\right)$, $s*\left(f\right)=sups>0:f\in B_{2,\infty }^s\left(ℝ\right)$. The existing results on estimation of smoothness [K. Dziedziul, M. Kucharska and B. Wolnik, J. Nonparametric Statist. 23 (2011)] employ the Haar basis and are limited to the case 0 < s*(f) < 1/2. Using p-regular (p ≥ 1) spline wavelets with exponential decay we extend them to density functions with 0 < s*(f) < p+1/2. Applying the Franklin-Strömberg wavelet p = 1, we prove that the presented estimator...