Bellman VS Beurling: sharp estimates of uniform convexity for $L^p$ spaces

Dmitriy M. Stolyarov; Paata Ivanisvili; Pavel B. Zatitskiy

arxiv: 1405.6229 · v1 · pith:COUSNXG6new · submitted 2014-05-23 · 🧮 math.CA · math.DG· math.FA

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

Paata Ivanisvili , Dmitriy M. Stolyarov , Pavel B. Zatitskiy This is my paper

classification 🧮 math.CA math.DGmath.FA

keywords bellmanconvexityestimatesfunctioninequalitiessharpspacesbeurling

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We obtain the classical Hanner inequalities by the Bellman function method. These inequalities give sharp estimates for the moduli of convexity of Lebesgue spaces. Easy ideas from differential geometry help us to find the Bellman function using neither "magic guesses" nor calculations.

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

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