= Wavelet coefficient decay for Hölder functions
Localized <wavelets> of support diameter $O(2^{-j})$ and $L^1$ <norm> $O(2^{-j/2})$, with enough <vanishing moments>, satisfy
$$
|\langle f,\psi_{j,n}\rangle|\le C\|f\|_{C^\alpha}2^{-j(\alpha+1/2)}.
$$
Subtract a <Taylor polynomial> annihilated by the <wavelet>, apply the <Hölder-Taylor remainder bound> on its <support of a function>, and multiply by its $L^1$ <norm>. The same argument applies to localized <boundary wavelets> with the same cancellation; finitely many coarse <scaling functions> are handled separately.
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