Boundary conditions for quasi-differential operators in L p spaces

For a very general class of ordinary quasi-differential expressions M with matrix-valued coefficients and for p, q ∈ 1, ∞) or p, q ∈ (1, ∞] all operators T of a subspace of LP into Lq which satisfy T _M ⁰ ? T ? Tm and are Fredholm operators with index zero are characterized by suitable boundary conditions, where Tm and T _M ⁰ are the maximal and minimal operators associated to M. This generalizes a result of Evans and Ibrahim for p = q = 2.