A characterisation of the rate of approximation of the Baskakov-Kantorovich operator

We characterise the $K$-functional that was previously shown to describe the rate of approximation of the Baskakov-Kantorovich operator in the $L_p$-spaces with the weight $(1+x)^\gamma$ with $\gamma\le 0$. The characterisation uses the Ditzian-Totik moduli of smoothness.