Sharp Kolmogorov Inequality between the L₂ᵣ-Norm of the Derivative, the Lᵣ-Norm of the Function, and the Asymmetric L_∞-Norm of the Second Derivative on the Real Line

In the paper, we find sharp constants in a Kolmogorov-type inequality between the L₂ᵣ -norm of the derivative, the Lᵣ -norm (quasinorm for $$r<1$$ ) of the function, and the asymmetric L_∞ -norm (including the norm of the nonnegative part) of the second derivative for any 1/2 ≤ r< ∞ on the real line and on the period.