A topology on inequalities

dc.contributor.authorD'Aristotile, Anna Maria
dc.contributor.authorFiorenza, Alberto
dc.date.accessioned2021-07-19T19:04:53Z
dc.date.available2021-07-19T19:04:53Z
dc.date.issued2006-08-02
dc.description.abstractWe 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.departmentMathematics
dc.formatText
dc.format.extent22 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationD'Aristotile, A. M., & Fiorenza, A. (2006). A topology on inequalities. <i>Electronic Journal of Differential Equations, 2006</i>(85), pp. 1-22.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13958
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectReal analysis
dc.subjectTopology
dc.subjectInequalities
dc.subjectHomogeneous operators
dc.subjectBanach spaces
dc.subjectOrlicz spaces
dc.subjectSobolev spaces
dc.subjectNorms
dc.subjectDensity
dc.titleA topology on inequalities
dc.typeArticle

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