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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Moreover, we study relationship between modulus of smoothness of the function and its de la Vallée-Poussin sums in these spaces.
📌 3 Key Takeaways
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Objective & Hypothesis:We investigate the approximation properties of the functions by trigonometric polynomials in weighted Lorentz spaces with weights satisfying so called Muckenhoupt's Ap condition.
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Key Findings & Data:Relations between moduli of smoothness of the derivatives of the functions and those of the functions itself are studied.
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Conclusion & Impact:Moreover, we study relationship between modulus of smoothness of the function and its de la Vallée-Poussin sums in these spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:moduli of smoothness · weighted Lorentz spaces · Muckenhoupt weight
Abstract
We investigate the approximation properties of the functions by trigonometric polynomials in weighted Lorentz spaces with weights satisfying so called Muckenhoupt's Ap condition. Relations between moduli of smoothness of the derivatives of the functions and those of the functions itself are studied. In weighted Lorentz spaces we also prove a theorem on the relationship between the derivatives of a polynomial of best approximation and the best approximation of the function. Moreover, we study relationship between modulus of smoothness of the function and its de la Vallée-Poussin sums in these spaces.
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Cite This Article
Jafarov, S. Z. (2016). On moduli of smoothness and approximation by trigonometric polynomials in weighted Lorentz spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 45 Issue: 6. https://ajindex.com/articles/1403073