Bellman VS. Beurling: sharp estimates of uniform convexity for 𝐿^{𝑝} spaces

Zatitskiy, P.; Ivanisvili, P.; Stolyarov, D.

doi:10.1090/spmj/1390

Bellman VS. Beurling: sharp estimates of uniform convexity for $L^p$ spaces
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by P. B. Zatitskiy, P. Ivanisvili and D. M. Stolyarov
Translated by: the authors

St. Petersburg Math. J. 27 (2016), 333-343

DOI: https://doi.org/10.1090/spmj/1390

Published electronically: January 29, 2016

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Abstract:

The classical Hanner inequalities are obtained by the Bellman function method. These inequalities give sharp estimates for the moduli of convexity of Lebesgue spaces, initially due to Clarkson and Beurling. Easy ideas from differential geometry make it possible to find the Bellman function by using neither “magic guesses” nor bulky calculations.

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