Let $\Omega $ be homogeneous of degree zero and have mean value zero on the unit sphere ${S}^{d-1}$ , $T_{\Omega }$ be the convolution singular integral operator with kernel $\frac {\Omega (x)}{|x|^d}$ . In this paper, we prove that if $\Omega \in L\log L(S^{d-1})$ , and U is an operator which is bounded on $L^2(\mathbb {R}^d)$ and satisfies the weak type endpoint estimate of $L(\log L)^{\beta }$ type, then the composition operator $UT_{\Omega }$ satisfies a weak type endpoint estimate of $L(\log L)^{\beta +1}$ type.

令 $\Omega $ 在单位球面 ${S}^{d-1}$ 上为零次齐次且均值为零， $T_{\Omega }$ 是卷积奇异积分算子，内核 $\frac { \Omega (x)}{|x|^d}$ 。在本文中，我们证明如果 $\Omega \in L\log L(S^{d-1})$ ，并且U是一个有界于 $L^2(\mathbb {R}^d) $ 并且满足 $L(\log L)^{\beta }$ 类型的弱类型端点估计，那么组合算子 $UT_{\Omega }$ 满足 $L(\log L)^的弱类型端点估计{\beta +1}$ 类型。