Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0<p≤1
- Albiac, Fernando 1
- Ansorena, José L. 2
- Cúth, Marek 3
- Doucha, Michal 4
- 1 Department of Mathematics, Statistics and Computer Sciences–InaMat2, Universidad Pública de Navarra, Campus de Arrosadía, 31006, Pamplona, Spain
- 2 Department of Mathematics and Computer Sciences, Universidad de La Rioja, 26004, Logroño, Spain
- 3 Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, 186 75, Praha 8, Czech Republic
- 4 Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic
ISSN: 0010-0757
Año de publicación: 2022
Volumen: 73
Fascículo: 3
Páginas: 337-357
Tipo: Artículo
Otras publicaciones en: Collectanea mathematica
Resumen
Our aim in this article is to contribute to the theory of Lipschitz free p-spaces for 0<p≤1 over the Euclidean spaces Rd and Zd. To that end, we show that Fp(Rd) admits a Schauder basis for every p∈(0,1], thus generalizing the corresponding result for the case p=1 by Hájek and Pernecká (J Math Anal Appl 416(2):629–646, 2014, Theorem 3.1) and answering in the positive a question that was raised by Albiac et al. in (J Funct Anal 278(4):108354, 2020). Explicit formulas for the bases of Fp(Rd) and its isomorphic space Fp([0,1]d) are given. We also show that the well-known fact that F(Z) is isomorphic to ℓ1 does not extend to the case when p<1, that is, Fp(Z) is not isomorphic to ℓp when 0<p<1.