@article{Babenko_Spector_2007, title={Estimates for wavelet coefficients on some classes of functions}, volume={59}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3415}, abstractNote={Let $ψ_m^D$ be orthogonal Daubechies wavelets that have $m$ zero moments and let $$W^k_{2, p} = \left\{f \in L_2(\mathbb{R}): ||(i \omega)^k \widehat{f}(\omega)||_p \leq 1\right\}, \;k \in \mathbb{N},$$. We prove that $$\lim_{m\rightarrow\infty}\sup\left\{\frac{|\psi^D_m, f|}{||(\psi^D_m)^{\wedge}||_q}: f \in W^k_{2, p} \right\} = \frac{\frac{(2\pi)^{1/q-1/2 }{\pi^k}\left(\frac{1 - 2^{1-pk }{pk -1}\right)^{1/p }{(2\pi)^{1/q-1/2 }.$$}, number={12}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Babenko, V. F. and Spector, S. A.}, year={2007}, month={Dec.}, pages={1594–1600} }