Beylkin-Coifman-Rokhlin (B-C-R)算法表明算子通常可用$2n$维小波来分析, 而本文用 基于$n$维小波来引入一种新方法考虑卷积型 Calder\'{o}n-Zygmund (C-Z)算子. 利用此方法来研究算子的逼近, 此逼近算法不仅比 B-C-R 算法简单而且有更快的逼近速度. 还证明了 H\"{o}rmander 条件能够保证算子在 Besov 空间${\dot{B}}_p^{0,q}(1\le p,q\le \mathrm{\infty })$ 和 Triebel--Lizorkin 空间$\dot{F}_p^{0,q}(1

Beylkin-Coifman-Rokhlin (B-C-R) algorithm says that an operator can be analyzed by 2n-dimensional wavelets, but here we provide a new method based on n-dimensional wavelets to consider convolution-type Calder\'{o}n-Zygmund (C-Z) operators. We apply this idea to the approximation; our approximation algorithm is much simpler than B-C-R algorithm and our approximation speed is much faster. By the way, we prove that H\"{o}rmander condition can ensure the continuity on Besov spaces ${\dot{B}}_p^{0,q}(1\le p,q\le \mathrm{\infty })$ and on Triebel-Lizorkin spaces $\dot{F}_p^{0,q}(1