Young's inequality and related results on time scales

We establish the classical Young inequality on time scales as follows: ab≤∫0agσ(x)Δx+∫0b(g−1)σ(y)Δy if g∈Crd([0,c],R) is strictly increasing with c>0 and g(0)=0,a∈[0,c],b∈[0,g(c)]. Using this inequality, we can extend Hőlder's inequality and Minkowski's inequality on time scales.