Geodesic
Probabilistic Proofs of the Little Riesz Theorem
Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 443-445

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The following theorem is a widely used corollary of the Thorn-Riesz convexity theorem ([1], pp. 526).Theorem. Let (Ω, a, μ) be a positive measure space, and let be a linear operator with ‖T‖1≤1, ‖T‖∞≤1. Then ‖T‖p≤1, 1≤p≤∞ 
Al-Hussaini, A. N. Probabilistic Proofs of the Little Riesz Theorem. Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 443-445. doi: 10.4153/CMB-1977-064-7
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     author = {Al-Hussaini, A. N.},
     title = {Probabilistic {Proofs} of the {Little} {Riesz} {Theorem}},
     journal = {Canadian mathematical bulletin},
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     year = {1977},
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     number = {4},
     doi = {10.4153/CMB-1977-064-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-064-7/}
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