Under some mild conditions on the functions ??{symbol}i and over(??{symbol}, ??)i (i ??? I), we establish the following result: If 0 < ?? < ?? < k, and if Q g = g for all polynomials of degree at most k - 1, then the estimate | f - Qh f |Bp, q?? ??? C h?? - ?? | f |Bp, q?? ??? f ??? Bp, q ?? (Rs) is valid for all h > 0, where C is a constant independent of h and f.