Bi-framelet systems with few vanishing moments characterize Besov spaces

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Dual Wavelet Frames and Riesz Bases in Sobolev Spaces (2009, background): “Characterization of the Sobolev norm and more general Besov norm of a function in terms of its weighted wavelet coefficient sequence has already been given in [2, 3, 41] using a pair of dual wavelet frames in L2(R), under the assumption that both wavelet frames must have certain required order of re”
Pairs of frequency-based nonhomogeneous dual wavelet frames in the distribution space (2009, background): “ty in (3.4), which is equivalent to the frame property in (3.5), characterizes the Sobolev space H−τ(R). We point out that the characterization of homogeneous Besov spaces by homogeneous framelets in [1, 15] uses nonlinear approximation and is quite diﬀerent in nature to (3.4) and (3.5). Now we are ”
On Multivariate Compactly Supported Bi-Frames (2007, background): “Moreover, wavelet bases, recently also wavelet frames, are applied to the characterization of function spaces, see for example [1, 13].”
A framelet-based image inpainting algorithm (2008, background): “The second example is from piecewise cubic B-spline whose refinement mask is h0 = 1 16 [1,4,6,4,1].”