EXPONENTIAL APPROXIMATION OF FUNCTIONS IN LEBESGUE SPACES WITH MUCKENHOUPT WEIGHT
R. Akgn ยท Problemy analiza ยท 2023
Using a transference result, several inequalities of approximation by entire functions of exponential type in ๐pRq, the class of bounded uniformly continuous functions defined on R -pยด8, `8q, are extended to the Lebesgue spaces ๐ฟ ๐ p๐๐๐ฅq 1 ๐ ฤ 8 with Muckenhoupt weight ๐.This gives us a different proof of Jackson type direct theorems and Bernstein-Timan type inverse estimates in ๐ฟ ๐ p๐๐๐ฅq.Results also cover the case ๐ " 1.