Tartar's method for the Riesz-Thorin interpolation theorem (Q1984247)

The author begins by stating the well-known Riesz-Thorin interpolation theorem, specifying the original contributions by Riesz in 1926 and by Thorin in 1948. After some more recent investigations concerning norm estimates, the author focuses his attention on an alternative proof of the Riesz-Thorin theorem by \textit{L. Tartar} [An introduction to Sobolev spaces and interpolation spaces. Berlin: Springer (2007; Zbl 1126.46001)] given for operators of strong types \((1, 1)\) and \((\infty,\infty)\), and extends his proof to operators of strong types \((p_1, q_1)\) and \((\infty,\infty)\) with \(1 \leq p_1 \leq q_1 < \infty\).