A note on polynomial approximation in Sobolev spaces

For domains which are star-shaped w.r.t. at least one point, we give new bo unds on the constants in Jackson-inequalities in Sobolev spaces. For convex domains, these bounds do not depend on the eccentricity. For non-convex do mains with a re-entrant corner, the bounds are uniform w.r.t. the exterior angle. The main tool is a new projection operator onto the space of polynom ials.