中文摘要：

In order to study the approximation by reciprocals of polynomials with real coefficients, one always assumes that the approximated function has a fixed sign on the given interval. Sometimes, the approximated function is permitted to have finite sign changes, such as l(l ≥ 1) times. Zhou Songping has studied the case l = 1 and l ≥ 2 in Lp spaces in order of priority. In this paper, we studied the case l ≥ 2 in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation.

英文摘要：

In order to study the approximation by reciprocals of polynomials with real coefficients, one always assumes that the approximated function has a fixed sign on the given interval. Sometimes, the approximated function is permitted to have finite sign changes, such as l（l ≥ 1） times. Zhou Songping has studied the case l=1 and l≥2 in L^p spaces in order of priority. In this paper, we studied the case l ≥2 in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation.