Estimates for wavelet coefficients on some classes of functions

• Datum: 2007
• Hauptverfasser: Babenko, V. F., Spector, S. A., Бабенко, В. Ф., Спектор, С. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2007
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3415
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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}||...