Best Constants between Equivalent Norms in Lorentz Sequence Spaces
We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ∥x∥(p,s):=inf{∑k∥x(k)∥p,s}, where the infimum is taken over all finite representations x=∑kx(k) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level seque...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/713534 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562276070064128 |
|---|---|
| author | S. Barza A. N. Marcoci L. E. Persson |
| author_facet | S. Barza A. N. Marcoci L. E. Persson |
| author_sort | S. Barza |
| collection | DOAJ |
| description | We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ∥x∥(p,s):=inf{∑k∥x(k)∥p,s}, where the infimum is taken over all finite representations x=∑kx(k) 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. |
| format | Article |
| id | doaj-art-88f1f876f0d64bbdab66d76075515b4e |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-88f1f876f0d64bbdab66d76075515b4e2025-02-03T01:23:06ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/713534713534Best Constants between Equivalent Norms in Lorentz Sequence SpacesS. Barza0A. N. Marcoci1L. E. Persson2Department of Mathematics, Karlstad University, 65188 Karlstad, SwedenDepartment of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020 396 Bucharest, RomaniaDepartment of Mathematics, Luleå University of Technology, 97 187 Luleå, SwedenWe find the best constants in inequalities relating the standard norm, the dual norm, and the norm ∥x∥(p,s):=inf{∑k∥x(k)∥p,s}, where the infimum is taken over all finite representations x=∑kx(k) 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.http://dx.doi.org/10.1155/2012/713534 |
| spellingShingle | S. Barza A. N. Marcoci L. E. Persson Best Constants between Equivalent Norms in Lorentz Sequence Spaces Journal of Function Spaces and Applications |
| title | Best Constants between Equivalent Norms in Lorentz Sequence Spaces |
| title_full | Best Constants between Equivalent Norms in Lorentz Sequence Spaces |
| title_fullStr | Best Constants between Equivalent Norms in Lorentz Sequence Spaces |
| title_full_unstemmed | Best Constants between Equivalent Norms in Lorentz Sequence Spaces |
| title_short | Best Constants between Equivalent Norms in Lorentz Sequence Spaces |
| title_sort | best constants between equivalent norms in lorentz sequence spaces |
| url | http://dx.doi.org/10.1155/2012/713534 |
| work_keys_str_mv | AT sbarza bestconstantsbetweenequivalentnormsinlorentzsequencespaces AT anmarcoci bestconstantsbetweenequivalentnormsinlorentzsequencespaces AT lepersson bestconstantsbetweenequivalentnormsinlorentzsequencespaces |