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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/713534 |
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| Summary: | 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. |
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| ISSN: | 0972-6802 1758-4965 |