Let $\mu$ be a Radon measure on ${{\rr}^d}$ which satisfies the growth condition only namely, there is a constant $C>0$ such that for all $x\in{{\rr}^d}$, $r>0$ and for some fixed $0<n\le d$, \[ \mu(B(x,r))\le Cr^n, \] where $B(x,r)$ is the ball centered at $x$ and having radius $r$. In this paper, we first give a new atomic characterization of the Hardy space $H^1(\mu)$ introduced by X. Tolsa. As applications of this new characterization, we establish the $(H^1(\mu),L^{1,\infty}(\mu))$ estimate of the commutators generated by $RBMO(\mu)$ functions with the Calderón–Zygmund operators whose kernels satisfy only the size condition and a certain minimum regularity condition. Using this endpoint estimate and a new interpolation theorem for operators which is also established in this paper and has independent interest, we further obtain the $L^p(\mu)$$(1<p<\infty)$ boundedness of these commutators.