Energy conditions in f(R, Lm) gravity

In order to constrain f(R, L-m) gravity from theoretical aspects, its energy conditions are derived in this paper. These energy conditions given by us are quite general and can be degenerated to the well-known energy conditions in general relativity and f(R) theories of gravity with arbitrary coupling, non-minimal coupling and non-coupling between matter and geometry, respectively, as special cases. To exemplify how to use these energy conditions to restrict f(R, L-m) gravity, we consider a special model in the FRW cosmology and give some corresponding results by using astronomical observations.