Extrapolation results on general Besov-Holder-Lipschitz spaces

General Besov-Holder-Lipschitz spaces Lambda (rho)(p,q) (IRn), where p is a n arbitrary q-admissible function, are introduced and extrapolation charact erizations concerning these spaces are given. We present some concrete exam ples and, in particular, we very easily obtain the extrapolation results [1 6, Proposition 2.5], [8, Proposition 4.2] and [14, Proposition 7]. New extr apolation results, as far as we are aware, concerning the spaces B-p,q((s, -b)) with s > 0, b greater than or equal to 0, 1 less than or equal to p le ss than or equal to +infinity and 0 < q less than or equal to +infinity are also given. We apply these extrapolation methods to give a different proof of some embeddings of certain Besov or Leopold spaces in spaces of Lipschi tz type proved by HAROSKE, Cf. [14, Proposition 11, Corollary 23 (i)]. We a lso improve [14, Proposition 11] when q = min(p, 2) and 1 less than or equa l to p less than or equal to +infinity, cf. Proposition 5.6.