“Compactly” supported frames for spaces of distributions on the ball

Frames are constructed on the unit ball Bd in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^d}$$\end{document} consisting of smooth functions with small shrinking supports. The new frames are designed so that they can be used for decomposition of weighted Triebel–Lizorkin and Besov spaces on Bd with weight \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${w_\mu(x):=(1-|x|^2)^{\mu-1/2}, \mu}$$\end{document} half integer, μ ≥ 0.