Weighted best local Lp approximation

AbstractFor a weight w with some conditions near the origin the limit of the error ε−n − 1{f(εt) − Pw,εf(εt)}, where Pw,εf is the weighted best Lw,εp approximation of the function f in a class tm,wp, analogous to those considered by Calderón and Zygmund, is characterized. The limit is taken in a norm depending on ε and, with additional assumptions on the weight, in a fixed norm