Inequalities with exponential weights

Let R=(-∞,∞)R=(-∞,∞) and let Q∈C2:R→R+=[0,∞)Q∈C2:R→R+=[0,∞) be an even function. Then in this paper we consider the infinite–finite range inequality, an estimate for the Christoffel function, and the Markov–Bernstein inequality with the exponential weights wρ(x)=|x|ρe-Q(x),x∈Rwρ(x)=|x|ρe-Q(x),x∈R.