Bellman VS Beurling: sharp estimates of uniform convexity for $L^p$ spaces
Classical Analysis and ODEs
2016-04-07 v1 Differential Geometry
Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1405.6229,
title = {Bellman VS Beurling: sharp estimates of uniform convexity for $L^p$ spaces},
author = {Paata Ivanisvili and Dmitriy M. Stolyarov and Pavel B. Zatitskiy},
journal= {arXiv preprint arXiv:1405.6229},
year = {2016}
}
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11 pages