Approximation properties of Bernstein's singular integrals in variable exponent Lebesgue spaces on the real axis

Abstract

In generalized Lebesgue spaces Lp(& BULL;) with variable exponent p (& BULL;) defined on the real axis, we obtain several inequalities of approximation by inte-gral functions of finite degree. Approximation properties of Bernstein singular integrals in these spaces are obtained. Estimates of simultaneous approxima-tion by integral functions of finite degree in Lp(& BULL;) are proved.