A topology on inequalities
| dc.contributor.author | D'Aristotile, Anna Maria | |
| dc.contributor.author | Fiorenza, Alberto | |
| dc.date.accessioned | 2021-07-19T19:04:53Z | |
| dc.date.available | 2021-07-19T19:04:53Z | |
| dc.date.issued | 2006-08-02 | |
| dc.description.abstract | We consider sets of inequalities in Real Analysis and construct a topology such that inequalities usually called "limit cases" of certain sequences of inequalities are in fact limits - in the precise topological sense - of such sequences. To show the generality of the results, several examples are given for the notions introduced, and three main examples are considered: Sequences of inequalities relating real numbers, sequences of classical Hardy's inequalities, and sequences of embedding inequalities for fractional Sobolev spaces. All examples are considered along with their limit cases, and it is shown how they can be considered as sequences of one "big" space of inequalities. As a byproduct, we show how an abstract process to derive inequalities among homogeneous operators can be a tool for proving inequalities. Finally, we give some tools to compute limits of sequences of inequalities in the topology introduced, and we exhibit new applications. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | D'Aristotile, A. M., & Fiorenza, A. (2006). A topology on inequalities. Electronic Journal of Differential Equations, 2006(85), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13958 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Real analysis | |
| dc.subject | Topology | |
| dc.subject | Inequalities | |
| dc.subject | Homogeneous operators | |
| dc.subject | Banach spaces | |
| dc.subject | Orlicz spaces | |
| dc.subject | Sobolev spaces | |
| dc.subject | Norms | |
| dc.subject | Density | |
| dc.title | A topology on inequalities | |
| dc.type | Article |