Geodesic
Exponential approximation of functions in Lebesgue spaces with Muckenhoupt weight
Problemy analiza, Tome 12 (2023) no. 1, pp. 3-24.

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Using a transference result, several inequalities of approximation by entire functions of exponential type in $\mathcal{C}(\mathbf{R})$, the class of bounded uniformly continuous functions defined on $\mathbf{R}:=\left(-\infty, +\infty \right)$, are extended to the Lebesgue spaces $L^{p}\left( \mathbf{\varrho }dx\right) $ $1\leq p\infty $ with Muckenhoupt weight $\mathbf{\varrho }$. This gives us a different proof of Jackson type direct theorems and Bernstein-Timan type inverse estimates in $L^{p}\left( \mathbf{\varrho }dx\right) $. Results also cover the case $p=1$.
Keywords: Muckenhoupt weight, entire functions of exponential type, one-sided Steklov operator, best approximation, direct theorem, inverse theorem, modulus of smoothness, Marchaud-type inequality, K-functional.
Mots-clés : Lebesgue spaces 
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R. Akgün. Exponential approximation of functions in Lebesgue spaces with Muckenhoupt weight. Problemy analiza, Tome 12 (2023) no. 1, pp. 3-24. http://geodesic.mathdoc.fr/item/PA_2023_12_1_a0/

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