Extrapolation results on general Besov-Hölder-Lipschitz spaces (Q2762266)

The author defines general Besov--Hölder--Lipschitz spaces \(\Lambda^{\rho}_{p,q}(\mathbb R^n)\) (\(1\leq p \leq \infty, 0<q \leq \infty\) and \(\rho\) is the so-called \(q\)--admissible function) and shows that particular choices of parameters involved yield either Besov or Hölder or Lipschitz spaces. Moreover, he provides an extrapolation description of spaces \(\Lambda^{\rho}_{p,q}(\mathbb R^n)\) and applies this result to give different proofs of certain embeddings of Besov--type spaces into Lipchitz spaces recently obtained by \textit{D. D. Haroske} [Z. Anal. Anwend. 19, 781--799 (2000; Zbl 0998.46013)].