In this paper, we study the existence of minimizers of the Sobolev quotient for a class of
nonlocal operators with an orthotropic structure having different exponents of integrability
and different orders of differentiability. Our method is based on the concentration-
compactness principle which we extend to this class of operators. One consequence of our
main result is the existence of a nontrivial nonnegative solution to the corresponding critical
problem.