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Extrapolation Results on General Besov‐Hölder‐Lipschitz Spaces
Author(s) -
Neves Júlio S.
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200110)230:1<117::aid-mana117>3.0.co;2-8
Subject(s) - proposition , lipschitz continuity , extrapolation , mathematics , corollary , besov space , pure mathematics , function space , mathematical analysis , interpolation space , functional analysis , epistemology , biochemistry , chemistry , gene , philosophy
General Besov ‐Hölder‐Lipschitz spaces $\Lambda ^\rho _{p,q}$ (ℝ n ), where ρ is an arbitrary q ‐admissible function, are introduced and extrapolation characterizations concerning these spaces are given. We present some concrete examples and, in particular, we very easily obtain the extrapolation results [16, Proposition 2.5], [8, Proposition 4.2] and [14, Proposition 7]. New extrapolation results, as far as we are aware, concerning the spaces $B^{(s,-b)} _{p,q}$ (ℝ n ), with s > 0, b ≥ 0, 1 ≤ p ≤ +∞ and 0 < q ≤ +∞ 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 Lipschitz type proved by Haroske , cf. [14, Proposition 11, Corollary 23 (i)]. We also improve [14, Proposition 11] when q = min( p , 2) and 1 ≤ p < +∞, cf. Proposition 5.6.