English

Sharp mutliplicative inequalities with $\mathrm{BMO}$ $\mathrm{I}$

Classical Analysis and ODEs 2020-01-28 v1

Abstract

We find the best possible constant CC in the inequality φLrCφLpprφBMO1pr\|\varphi\|_{L^r}\leq C\|\varphi\|_{L^p}^{\frac{p}{r}}\|\varphi\|_{\mathrm{BMO}}^{1-\frac{p}{r}}, where 2r2 \leq r and p<rp < r. We employ the Bellman function technique to solve this problem in the case of an interval and then transfer our results to the circle and the line.

Keywords

Cite

@article{arxiv.2001.09454,
  title  = {Sharp mutliplicative inequalities with $\mathrm{BMO}$ $\mathrm{I}$},
  author = {Dmitriy Stolyarov and Vasily Vasyunin and Pavel Zatitskiy},
  journal= {arXiv preprint arXiv:2001.09454},
  year   = {2020}
}

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17 pages