Christoffel-type functions for m-orthogonal polynomials for Freud weights

This paper gives upper and lower bounds of the Christoffel-type functions @l"j"n(W^m,m;x),j=m-2,m-4,...,m-2[m/2], for the m-orthogonal polynomials for a Freud weight W=e^-^Q, which are given as follows. Let a"n=a"n(Q) be the nth Mhaskar-Rahmanov-Saff number, @f"n(x)=max{n^-^2^/^3,1-|x|/a"n}, and d>0. Assume that Q@?C(R) is even, Q^''@?C[0,~),Q^'(x)>0,x@?(0,~),Q(0)=0, and for some A,B>1A=<(xQ^'(x))^'Q^'(x)==ca"nn^j^+^1W(x)^m@f"n(x)^-^1^/^2,miseven,j=0,ca"nn^j^+^1W(x)^motherwise,and for |x|=