Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0 < p≤ 1

0560291 - MÚ 2023 RIV ES eng J - Článek v odborném periodiku
Albiac, F. - Ansorena, J.L. - Cúth, M. - Doucha, Michal
Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0 < p≤ 1.
Collectanea Mathematica. Roč. 73, č. 3 (2022), s. 337-357. ISSN 0010-0757. E-ISSN 2038-4815
Grant CEP: GA ČR(CZ) GX20-31529X
Institucionální podpora: RVO:67985840
Klíčová slova: isomorphic theory of Banach spaces * Lp-space * Lipschitz free p-space * Lipschitz free space * quasi-Banach space
Obor OECD: Pure mathematics
Impakt faktor: 1.1, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1007/s13348-021-00322-9

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.
Trvalý link: https://hdl.handle.net/11104/0333273