A simple proof of the real Riesz–Thorin interpolation theorem in the lower triangle

A simple proof of the real Riesz–Thorin interpolation theorem for operators of strong types $(p_0, q_0)$ and $(\infty , \infty )$ in the lower triangle, that is, if $0 \lt p_0 \leq q_0 \lt \infty $ with the best estimate of the norms is presented.