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Sep 14, 2021 at 6:24 vote accept J.Mayol
Sep 7, 2021 at 15:52 comment added Mark Lewko The answer turns out to be negative. I've adjusted my answer accordingly.
Sep 7, 2021 at 2:42 history edited Mark Lewko CC BY-SA 4.0
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Sep 3, 2021 at 3:47 comment added Mark Lewko Sorry I misread your question. I was thinking of Hardy and Littlewood's proof that characters are the only extremals to the Hausdorff-Young inequality on the circle, which includes an analysis of a question similar to yours.
Sep 2, 2021 at 9:40 comment added J.Mayol I searched Zygmund's books but did not find anything.
Sep 1, 2021 at 6:43 comment added J.Mayol Thank you. Do you know in which Chapter it is located (Trigonometric Series is about 600 pages long!)
Aug 31, 2021 at 16:44 history answered Mark Lewko CC BY-SA 4.0