Exponential approximation of functions in lebesgue spaces with muckenhoupt weight

Abstract

Using a transference result, several inequalities of ap-proximation by entire functions of exponential type in C(R), the class of bounded uniformly continuous functions defined on R - (-oo, +oo), are extended to the Lebesgue spaces Lp (gdx) 1 < p < oo with Muckenhoupt weight g. This gives us a different proof of Jackson type direct theorems and Bernstein-Timan type inverse estimates in Lp (gdx). Results also cover the case p = 1.