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Discrete characterisations of Lipschitz spaces on fractals
Author(s) -
Bodin Mats
Publication year - 2009
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/mana.200610720
Subject(s) - mathematics , lipschitz continuity , smoothness , pure mathematics , besov space , fractal , class (philosophy) , sequence (biology) , order (exchange) , type (biology) , mathematical analysis , interpolation space , functional analysis , computer science , biochemistry , chemistry , genetics , finance , artificial intelligence , biology , economics , gene , ecology
A. Kamont has discretely characterised Besov spaces on intervals. In this paper, we give a discrete characterisation of Lipschitz spaces on fractals admitting a type of regular sequence of triangulations, and for a class of post critically finite self‐similar sets. This shows that on some fractals, certain discretely defined Besov spaces, introduced by R. Strichartz, coincide with Lipschitz spaces introduced by A. Jonsson and H. Wallin for low order of smoothness. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)