English

Sharp L^p estimates on BMO

Classical Analysis and ODEs 2011-10-11 v1

Abstract

We construct the upper and lower Bellman functions for the LpL^p (quasi)-norms of BMO functions. These appear as solutions to a series of Monge--Amp\`ere boundary value problems on a non-convex plane domain. The knowledge of the Bellman functions leads to sharp constants in inequalities relating average oscillations of BMO functions and various BMO norms.

Keywords

Cite

@article{arxiv.1110.1771,
  title  = {Sharp L^p estimates on BMO},
  author = {Leonid Slavin and Vasily Vasyunin},
  journal= {arXiv preprint arXiv:1110.1771},
  year   = {2011}
}

Comments

42 pages, 12 figures

R2 v1 2026-06-21T19:17:20.560Z