  We discuss the process $p+p\to h_1+h_2+X$, where the identified hadrons $h_1$
and $h_2$ have large transverse momenta and are produced in high-energy
proton-proton collisions with a large rapidity gap between them. In this case
the (calculable) hard part of the reaction receives large higher order
corrections $\sim \alpha^n_s\ln^n \Delta y$, which can be accounted for in the
BFKL approach. Specifically, we describe in the next-to-leading order the
calculation of the vertex (impact-factor) for the inclusive production of the
identified hadron.
