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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In particular, the orders of approximation of Zygmund and Abel-Poisson means of Fourier trigonometric series were estimated by the $k-th$~modulus of smoothness in reflexive weighted Orlicz spaces with Muckenhoupt weights.
📌 3 Key Takeaways
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Objective & Hypothesis:In the present work, we investigate estimates of the deviations of the periodic functions from the linear operators constructed on the basis of its Fourier series in reflexive weighted Orlicz spaces with Muckenhoupt weights.
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Key Findings & Data:In the present work, we investigate estimates of the deviations of the periodic functions from the linear operators constructed on the basis of its Fourier series in reflexive weighted Orlicz spaces with Muckenhoupt weights.
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Conclusion & Impact:In particular, the orders of approximation of Zygmund and Abel-Poisson means of Fourier trigonometric series were estimated by the $k-th$~modulus of smoothness in reflexive weighted Orlicz spaces with Muckenhoupt weights.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Boyd indices · weighted Orlicz space · Muckenhoupt weight
Abstract
In the present work, we investigate estimates of the deviations of the periodic functions from the linear operators constructed on the basis of its Fourier series in reflexive weighted Orlicz spaces with Muckenhoupt weights. In particular, the orders of approximation of Zygmund and Abel-Poisson means of Fourier trigonometric series were estimated by the $k-th$~modulus of smoothness in reflexive weighted Orlicz spaces with Muckenhoupt weights.
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Cite This Article
JAFAROV, S. (2018). Linear methods of summing Fourier series and approximation in weighted Orlicz spaces. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 6, 2916–2925. https://ajindex.com/articles/220592