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Best constants between equivalent norms in Lorentz sequence spaces
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2012 (English)In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 2012Article in journal (Refereed) Published
Abstract [en]

We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ‖ 푥 ‖ ( 푝 , 푠 ) ∑ ∶ = i n f { 푘 ‖ 푥 ( 푘 ) ‖ 푝 , 푠 } , where the infimum is taken over all finite representations ∑ 푥 = 푘 푥 ( 푘 ) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.

Place, publisher, year, edition, pages
2012. Vol. 2012
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-12125DOI: 10.1155/2012/713534ISI: 000301411000001Scopus ID: 2-s2.0-84864930909Local ID: b31ae66d-3ac3-475e-abab-8a231cb0dcedOAI: oai:DiVA.org:ltu-12125DiVA, id: diva2:985075
Note
Validerad; 2012; Bibliografisk uppgift: Article ID 713534; 20120309 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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