Convex polynomial approximation in $R^d$ with Freud weights

Oleksandr Maizlish, Andriy Prymak

We show that for multivariate Freud-type weights $W_{\alpha }(x)=\exp (-|x{|}^{\alpha })$, $\alpha >1$, any convex function $f$ on $R^d$ satisfying $f{W}_{\alpha }\in L_p(R^d)$ if $1\le p<\infty$, or $\lim_{|x|\to\i…