Let \(10} \Biggl(|B(r)|^{-1} \int_{B(r)}|f(x)-f_{B(r)}|^pdx\Biggr)^{1/p}<\infty, \] where \(f_{B(r)}\) is the integral mean of \(f\) over the ball \(B(r)\) with center at the origin and radius \(r\). This space is a local version of the usual \(\text{BMO}(\mathbb{R}^n)\), and a dual space of a kind of Hardy space associated with the Herz space. The authors give a characterization of \(\text{CBMO}_2(\mathbb{R}^n)\) in terms of the central Carleson measure. Using this, they give some results on \(\text{CBMO}_2(\mathbb{R}^n)\) boundedness of several classes of general Littlewood-Paley operators.