Weak compactness in variable exponent spaces
| dc.contributor.author | Hernández, Francisco L. | |
| dc.contributor.author | Ruiz Bermejo, César | |
| dc.contributor.author | Sanchiz, Mauro | |
| dc.date.accessioned | 2023-06-17T09:05:59Z | |
| dc.date.available | 2023-06-17T09:05:59Z | |
| dc.date.issued | 2021 | |
| dc.description | CRUE-CSIC (Acuerdos Transformativos 2021) | |
| dc.description.abstract | This paper shows necessary and sufficient conditions on subsets of variable exponent spaces Lp(·)(Ω) in order to be weakly compact. Useful criteria are given extending Andô results for Orlicz spaces. As application, we prove that all separable variable exponent spaces are weakly Banach-Saks. Also, L-weakly compact and weakly compact inclusions between variable exponent spaces are studied. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/65756 | |
| dc.identifier.doi | 10.1016/j.jfa.2021.109087 | |
| dc.identifier.issn | 0022-1236 | |
| dc.identifier.officialurl | https://doi.org/10.1016/j.jfa.2021.109087 | |
| dc.identifier.relatedurl | https://www.sciencedirect.com/science/article/pii/S0022123621001695#! | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/8166 | |
| dc.issue.number | 6 | |
| dc.journal.title | Journal of Functional Analysis | |
| dc.language.iso | eng | |
| dc.page.initial | 109087 | |
| dc.publisher | Elsevier | |
| dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/es/ | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Variable exponent Lebesgue spaces | |
| dc.subject.keyword | Weak compactness | |
| dc.subject.keyword | Equi-integrability | |
| dc.subject.keyword | Weak Banach-Saks property | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Weak compactness in variable exponent spaces | |
| dc.type | journal article | |
| dc.volume.number | 281 | |
| dcterms.references | [1]F. Albiac, N. Kalton, Topics in Banach Space Theory, Springer, 2006. [2]T. Andô, Weakly compact sets in Orlicz spaces, Can. J. Math. 14 (1962) 170–176. [3]D. Cruz-Uribe, A. Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis, Birkhäuser, Basel, 2013. [4]C.J. dela ValléePoussin, Sur l’intégrale de lebesgue, Trans. Am. Math. Soc. 16 (1912) 435–501. [5]L. Diening, P. Harjulehto, P. Hästö, M. Ružička, Lebesgue and Sobolev Spaces with Variable Ex-ponents, Lecture Notes in Math., vol.2017, 2011. [6]J. Diestel, Sequences and Series in Banach Spaces, Springer, 1984. [7]P.G. Dodds, F.A. Sukochev, G. Schlüchtermann, Weak compactness criteria in symmetric spaces of measurable operators, Math. Proc. Camb. Philos. Soc. 131 (2001) 363- 384. [8]B. Dong, Z. Fu, J. Xu, Riesz-Kolmogorov theorem in variable exponent Lebesgue spaces and its applications to Riemann-Liouville fractional differential equations, Sci. China Math. 61 (2018) 1807–1824. [9]J. Flores, F.L. Hernández, C. Ruiz, M. Sanchiz, On the structure of variable exponent spaces, Indag. Math. 31 (2020) 831–841. [10]J. Flores, C. Ruiz, Domination by positive Banach-Saks operators, Stud. Math. 173 (2006) 185–192. [11]P. Górka, R. Bandaliyev, Relatively compact sets in variable-exponent Lebesgue spaces, Banach J. Math. Anal. 12 (2018) 331–346. [12]P. Górka, A. Macios, Almost everything you need to know about relatively compact sets in variable Lebesgue spaces, J. Funct. Anal. 269 (2015) 1925–1949. [13]P. Harjulehto, P. Hästö, Orlicz Spaces and Generalized Orlicz Spaces, Lecture Notes in Math., vol.2236, Springer, 2019. [14]F.L. Hernández, C. Ruiz, �q-structure of variable exponent spaces, J. Math. Anal. Appl. 389 (2012) 899–907. [15]F.L. Hernández, Y. Raynaud, E.M. Semenov, Bernstein widths and super strictly singular inclusions, Oper. Theory, Adv. Appl. 218 (2012) 359–376. [16]J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces II, Springer-Verlag, 1979. [17]J. Lukes, L. Pick, D. Pokorný, On geometric properties of the spaces Lp(x), Rev. Mat. Complut. 24 (2011) 115–130. [18]P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, Berlin, Heidelberg, 1991. [19]J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math., vol.1034, Springer, 1983. [20]M. Nowak, Weak compactness in Köthe-Bocher spaces and Orlicz-Bocher spaces, Indag. Math. 10 (1999) 73–86. [21]M.M. Rao, Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, Inc., New York, 1991. [22]M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math., vol.1748, Springer, 2001. [23]W. Szlenk, Sur les suites faiblements convergentes dans l’espace L, Stud. Math. 25 (1965) 337–341. [24]L. Weis, Banach lattices with the subsequence splitting property, Proc. Am. Math. Soc. 105 (1989) 87–96. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 99883408-190b-4f61-be14-23d8126a2710 | |
| relation.isAuthorOfPublication.latestForDiscovery | 99883408-190b-4f61-be14-23d8126a2710 |
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