Feller semigroups, L-p-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols

The question of extending L-p-sub-Markovian semigroups to the spaces L-q, q > P, and the interpolation of LP-sub-Markovian semigroups with Feller semi groups is investigated. The structure of generators of L-p-sub-Markovian se migroups is studied. Subordination in the sense of Bochner is used to discu ss the construction of refinements of L-p-sub-Markovian semigroups. The rol e played by some function spaces which are domains of definition for L-p-ge nerators is pointed out. The problem of regularising powers of generators a s well as some perturbation results are discussed.