Counterexample to Carbery's Sharpened Triangle Inequality in Lp Spaces
A new paper on arXiv (2605.05192) presents a counterexample to a sharpened form of the triangle inequality proposed by Carbery for Lp spaces with p>2. The inequality, which aimed to bound the norm of a sum of functions, is shown to fail for every p>2. The authors also prove that if such an estimate holds, the exponent c must satisfy c ≤ p', and they establish the inequality at the critical exponent c=p' for all integer p≥2. Additionally, a sharp three-function bound is obtained for p≥3. The work is purely mathematical and has no direct application to art.
Key facts
- Paper arXiv:2605.05192 submitted to arXiv
- Carbery proposed a sharpened triangle inequality for Lp spaces
- Counterexample constructed for every p>2
- Exponent condition c ≤ p' proven
- Inequality established at critical exponent c=p' for integer p≥2
- Sharp three-function bound obtained for p≥3
- No art-related content
Entities
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