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Isomorphic classification of mixed sequence spaces and of Besov spaces over [0, 1] d

2016; Wiley; Volume: 290; Issue: 8-9 Linguagem: Inglês

10.1002/mana.201600236

1522-2616

Fernando Albiac, José L. Ansorena,

Advanced Harmonic Analysis Research

Mathematische NachrichtenVolume 290, Issue 8-9 p. 1177-1186 Original Paper Isomorphic classification of mixed sequence spaces and of Besov spaces over [0, 1]d Fernando Albiac, Corresponding Author Fernando Albiac fernando.albiac@unavarra.es Mathematics Department, Public University of Navarre, Pamplona, 31006 SpainCorresponding author: e-mail: fernando.albiac@unavarra.es, Phone: +34 948 169 553, Fax: +34 948 166 057Search for more papers by this authorJosé Luis Ansorena, José Luis Ansorena joseluis.ansorena@unirioja.es +34 941 299 464, | Fax: +34 941 299 460 Department of Mathematics and Computer Science, University of La Rioja, Logroño, 26004 SpainSearch for more papers by this author Fernando Albiac, Corresponding Author Fernando Albiac fernando.albiac@unavarra.es Mathematics Department, Public University of Navarre, Pamplona, 31006 SpainCorresponding author: e-mail: fernando.albiac@unavarra.es, Phone: +34 948 169 553, Fax: +34 948 166 057Search for more papers by this authorJosé Luis Ansorena, José Luis Ansorena joseluis.ansorena@unirioja.es +34 941 299 464, | Fax: +34 941 299 460 Department of Mathematics and Computer Science, University of La Rioja, Logroño, 26004 SpainSearch for more papers by this author First published: 12 October 2016 https://doi.org/10.1002/mana.201600236Citations: 3Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The aim of this paper is to establish the isomorphic classification of Besov spaces over [0, 1]d. Using the identification of the Besov space with the -infinite direct sum of finite-dimensional spaces (which holds independently of the dimension and of the smoothness degree of the space ) we show that , , is a family of mutually non-isomorphic spaces. The only exception is the isomorphism between the spaces and , which follows from Pełczyński's isomorphism between and . We also tell apart the isomorphic classes of spaces from the isomorphic classes of Besov spaces over the Euclidean space . Citing Literature Volume290, Issue8-9June 2017Pages 1177-1186 RelatedInformation