We develop the theory of weak Hardy spaces H1,\infty on space of homogeneous type. As some applications, we show that certain singular integral operators and fractional integral operators are bounded from H1,\infty to L1,\infty and L\frac{1}{1-a},\infty, respectively. We give also the endpoint estimates for Nagel and Stein's singular integrals studied in [10].

We develop the theory of weak Hardy spaces H1,\infty on space of homogeneous type. As some applications, we show that certain singular integral operators and fractional integral operators are bounded from H1,\infty to L1,\infty and L\frac{1}{1-a},\infty, respectively. We give also the endpoint estimates for Nagel and Stein's singular integrals studied in [10].