This article is cited in 2 papers

Exponential approximation of functions in Lebesgue spaces with Muckenhoupt weight

R. Akgün

Balikesir University, Faculty of Arts and Sciences, Department of Mathematics, Cagis Yerleskesi, Altieylul, 10145, Balikesir, Türkiye

Abstract: 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: Lebesgue spaces, 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.

UDC: 517.518, 517.982.256

MSC: 41A10, 41A25, 41A27, 41A65, 41A81

Received: 29.08.2022
Revised: 09.12.2022
Accepted: 16.12.2022

Language: English

DOI: 10.15393/j3.art.2023.12250

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