Weighted best local \(L^ p\) approximation (Q1059798)

For a weight w with some conditions near the origin the limit of the error \(\epsilon^{-n-1}\{f(\epsilon t)-P_{w,\epsilon}f(\epsilon t)\}\), where \(P_{w,\epsilon}f\) is the weighted best \(L^ p_{w,\epsilon}\) approximation of the function f in a class \(t^ p_{m,w}\), analogous to those considered by Calderón and Zygmund, is characterized. The limit is taken in a norm depending on \(\epsilon\) and, with additional assumptions on the weight, in a fixed norm.