Exponential approximation of functions in Lebesgue spaces with Muckenhoupt weight

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 $L^p\left(\varrho dx\right)$ $1\le p<\infty$ with Muckenhoupt weight $\varrho$ ($1\le p<\infty$). This gives us a different proof of Jackson type direct theorems and Bernstein-Timan type inverse estimates in $L^p\left(\varrho dx\right)$. Results also cover the case $p=1$.

arXiv comment18 pages, Submitted. arXiv admin note: text overlap with arXiv:2109.02083