RESOLVENT ESTIMATES FOR SINGULARLY PERTURBED ELLIPTIC-OPERATORS IN HOLDER SPACES

The norm of the inverse operator of epsilon A + B - lambda I between t he Besov spaces B-infinity,infinity(s)(Omega) and B-infinity,infinity( t)(Omega) is estimated, where A and B are uniformly elliptic operators with smooth coefficients and Dirichlet boundary conditions, A is of o rder 2m, B of order 2m', m > m'. The estimate holds for negative t. Th e Besov space B-infinity,infinity(s)(Omega) reduces to the space of Ho lder continuous functions C-s (<(Omega)over bar>) if s > 0 is non-inte ger. In particular, is shown A(epsilon) generates an analytic semigrou p in B-infinity,infinity(s)(Omega), s is an element of (-1,0), if Omeg a = R(n) or R(+)(n) and A, B are constant coefficient operators withou t lower terms.