Estimates for wavelet coefficients on some classes of functions - Babenko, V. F.; Spector, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
Let $ψ_m^D$ be orthogonal Daubechies wavelets that have $m$ zero moments and let $$W^k_{2, p} = \left\{f \in L_2(\mathbb{R}): ||(i ω)^k \widehat{f}(ω)||_p ≤ 1\right\}, \;k \in \mathbb{N},$$. We prove that $$\lim_{m→∞}\sup\left\{\frac{|ψ^D_m, f|}{||(ψ^D_m)^{\wedge}||_q}: f \in W^k_{2, p} \right\} = \frac{\frac{(2π)^{1/q-1/2}}{π^k}\left(\frac{1 - 2^{1-pk}}{pk -1}\right)^{1/p}}{(2π)^{1/q-1/2}}.$$