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Abstract Although wavelet decompositions of functions in Besov spaces have been extensively investigated, those involved with mild decay bases are relatively unexplored. In this paper, we study wavelet bases of Besov spaces and the relation between norms and wavelet coefficients. We establish the l p $l^{p}$ -stability as a measure of how effectively the Besov norm of a function is evaluated by its wavelet coefficients and the L p $L^{p}$ -completeness of wavelet bases. We also discuss wavelets with decay conditions and establish the Jackson inequality.