Ul'yanov-type inequality for bounded convex sets in Rd

For @[email protected]?R^d, a convex bounded set with non-empty interior, the moduli of smoothness @w^r(f,t)"L"""q"("@W") and the norm @[email protected]?"L"""q"("@W") are estimated by an Ul'yanov-type expression involving @w^r(f,t)"L"""p"("@W") where 0