Factorization in rings of integer-valued rational functions

For a domain D, the ring Int(D) of integer-valued polynomials over D is atomic if D satisfies the ascending chain condition on principal ideals. However, even for a discrete valuation domain V, the ring IntR(V) of integer-valued rational functions over V is antimatter. We introduce a family of atomic rings of integer-valued rational functions and study various factorization properties in these rings.