Interpolation properties of Besov spaces defined on metric spaces

0339255 - MÚ 2010 RIV DE eng J - Journal Article
Gogatishvili, Amiran - Koskela, P. - Shanmugalingam, N.
Interpolation properties of Besov spaces defined on metric spaces.
Mathematische Nachrichten. Roč. 283, č. 2 (2010), s. 215-231. ISSN 0025-584X. E-ISSN 1522-2616
R&D Projects: GA ČR GA201/05/2033; GA ČR GA201/08/0383
Institutional research plan: CEZ:AV0Z10190503
Keywords : Besov spaces * Sobolev spaces * real interpolation method * K-functional * metric measure space * doubling measure space * embedding theorems
Subject RIV: BA - General Mathematics
Impact factor: 0.653, year: 2010
http://onlinelibrary.wiley.com/doi/10.1002/mana.200810242/abstract;jsessionid=144DA4B489B3CA8F4C6A08EF8BD172FE.f03t04

Let X = (X, d, μ) be a doubling metric measure space. We define so called Besov spaces B_{p,q}^α(X). We will show that if a doubling metric measure space (X, d, μ) supports a (1, p)-Poincaré inequality, then the Besov space B_{p,q}^α(X) coincides with the real interpolation space (L_{p}(X), KS_{1,p}(X))_{ α ,q}, where KS_{1,p}(X) is the Sobolev space defined by Korevaar and Schoen . This result is used to prove the imbedding theorems.
Permanent Link: http://hdl.handle.net/11104/0182837