End-point Norm Estimates for Cesàro and Copson Operators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| author | Barza, Sorina Demissie, Bizuneh Minda Sinnamon, Gord |
| author_facet | Barza, Sorina Demissie, Bizuneh Minda Sinnamon, Gord |
| contents | For a large class of operators acting between weighted $\ell^\infty$ spaces, exact formulas are given for their norms and the norms of their restrictions to the cones of nonnegative sequences; nonnegative, nonincreasing sequences; and nonnegative, nondecreasing sequences. The weights involved are arbitrary nonnegative sequences and may differ in the domain and codomain spaces. The results are applied to the Cesàro and Copson operators, giving their norms and their distances to the identity operator on the whole space and on the cones. Simplifications of these formulas are derived in the case of these operators acting on power-weighted $\ell^\infty$. As an application, best constants are given for inequalities relating the weighted $\ell^\infty$ norms of the Cesàro and Copson operators both for general weights and for power weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01988 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | End-point Norm Estimates for Cesàro and Copson Operators Barza, Sorina Demissie, Bizuneh Minda Sinnamon, Gord Functional Analysis 26D15 (Primary) 47B37 (Secondary) For a large class of operators acting between weighted $\ell^\infty$ spaces, exact formulas are given for their norms and the norms of their restrictions to the cones of nonnegative sequences; nonnegative, nonincreasing sequences; and nonnegative, nondecreasing sequences. The weights involved are arbitrary nonnegative sequences and may differ in the domain and codomain spaces. The results are applied to the Cesàro and Copson operators, giving their norms and their distances to the identity operator on the whole space and on the cones. Simplifications of these formulas are derived in the case of these operators acting on power-weighted $\ell^\infty$. As an application, best constants are given for inequalities relating the weighted $\ell^\infty$ norms of the Cesàro and Copson operators both for general weights and for power weights. |
| title | End-point Norm Estimates for Cesàro and Copson Operators |
| topic | Functional Analysis 26D15 (Primary) 47B37 (Secondary) |
| url | https://arxiv.org/abs/2211.01988 |