Ul’yanov-type inequality for bounded convex sets in RdRd

For Ω∈RdΩ∈Rd, a convex bounded set with non-empty interior, the moduli of smoothness ωr(f,t)Lq(Ω)ωr(f,t)Lq(Ω) and the norm ∥f∥Lq(Ω)∥f∥Lq(Ω) are estimated by an Ul’yanov-type expression involving ωr(f,t)Lp(Ω)ωr(f,t)Lp(Ω) where 0