Wavelet packet approximation theorem forHrtype norm

In this paper, we give the wavelet packet approximation theorem for Hr type norm which can measure difference of the (weak) derivatives. We will show that with equal distribution of the vanishing moments between the scaling function ω0 and the wavelet packets ωn,n∈N, if the sample values of a smooth function as scaling function coefficients at a fine scale are used, then the wavelet packet series approximates the smooth function under consideration with increasing verity in Hr type norm as the number of vanishing moments M increases or the scale J gets finer.