Characterization of Function Spaces Using Wavelets

It is well known that we can use wavelets to characterize various function spaces, for example, Lebesgue, Sobolev, and Besov spaces, and get equivalent norms with wavelet coefficients. However, we cannot determine whether a function is in these spaces by looking only at the wavelet coefficients since the constant function is orthogonal to all wavelets. In this paper, we close the gap by investigating the convergence of wavelet series.