Jackson Theorems for Erdős Weights inLp(0

An Erdős weight is of the formW≔e−QwhereQis even and of faster than polynomial growth at ∞. For example, we can takeQ(x)≔expk(|x|α), k⩾1, α>0, x∈R,where expkdenotes thekth iterated exponential. We prove Jackson theorems in weightedLpspaces with norm ‖fW‖Lp(R)for all 0