On solvability of a general elliptic boundary value problem in Hölder — Zygmund spaces with variable smoothness

Fredholm solvability of an elliptic boundary value problem, corresponding to the Green operator from the L. Boutet de Monvel algebra on a smooth manifold with compact boundary is studied in the paper. The Hölder — Zygmund spaces with variable smoothness are considered as function spaces. Sufficient conditions are given for the Fredholm property of the Green operator from the considered algebra in such spaces.