Sharp Ul’yanov-type inequalities using fractional smoothness

In this paper we obtain the following sharp (p,q)(p,q) inequalities for moduli of smoothness of fractional order: ωk(f,δ)Lq(X)⩽C(∫0δ(t−θωk+θ(f,t)Lp(X))qdtt)1q,1