Interpolation between Sobolev and between Lipschitz spaces of analytic functions on starshaped domains Academic Article

We show that on a starshaped domain Omega in C n {operatorname {C} ^n} (actually on a somewhat larger, biholomorphically invariant class) the L p {mathcal {L}^p} -Sobolev spaces of analytic functions form an interpolation scale for both the real and complex methods, for each p , 0 > p p,;0 > p leqslant infty . The case p = p = infty gives the Lipschitz scale; here the functor ( , ) [ ] {(,)^{[ heta ]}} has to be considered (rather than ( , ) [ ] {(,)_{[ heta ]}} ).