Exponential approximation of functions in Lebesgue spaces with Muckenhoupt weight

2022/08/29 by Akgün, Ramazan
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.13396

Abstract

Using a transference result, several inequalities of approximation by entire functions of exponential type in C(R), the class of bounded uniformly continuous functions defined on R:=( -∞ ,+∞ ) , are extended to the Lebesgue spaces L^p( \varrho dx) 1≤ p<∞ with Muckenhoupt weight \varrho (1≤ p<∞ ). This gives us a different proof of Jackson type direct theorems and Bernstein-Timan type inverse estimates in L^p( \varrho dx) . Results also cover the case p=1.

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