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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We prove an equivalence between the mixed modulus of continuity and K -functional and realization functional.
📌 3 Key Takeaways
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Objective & Hypothesis:Main properties of the mixed modulus of continuity in the Lebesgue spaces with Muckenhoupt weights are investigated.
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Key Findings & Data:We use the mixed modulus of continuity to obtain Potapov type direct and inverse estimates of angular trigonometric approximation of functions in these spaces.
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Conclusion & Impact:We prove an equivalence between the mixed modulus of continuity and K -functional and realization functional.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Direct theorem · inverse theorem · Muckenhoupt weights
Abstract
Main properties of the mixed modulus of continuity in the Lebesgue spaces with Muckenhoupt weights are investigated. We use the mixed modulus of continuity to obtain Potapov type direct and inverse estimates of angular trigonometric approximation of functions in these spaces. We prove an equivalence between the mixed modulus of continuity and K -functional and realization functional.
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Cite This Article
AKGÜN, R. (2022). Mixed modulus of continuity in the Lebesgue spaces with Muckenhoupt weights and their properties. Turkish Journal of Mathematics, Cilt: 40 - Sayı: 6, 1169–1192. https://ajindex.com/articles/608198