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We present characterizations of the Besov-type spaces B s,τ p,q and the Triebel-Lizorkin-type spaces F s,τ p,q by differences. All these results generalize the existing classical results on Besov and Triebel-Lizorkin spaces by taking τ 0.doi:10.1155/2012/328908 fatcat:mkxxput3inhurelqyjfp4ryfxi