Sharp L^p estimates on BMO

2011/10/08 by Slavin, Leonid, Vasyunin, Vasily
#42A05 #42B35 #49K20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1110.1771

Abstract

We construct the upper and lower Bellman functions for the L^p (quasi)-norms of BMO functions. These appear as solutions to a series of Monge--Ampère 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.

Related

• Sharp results in the integral-form John--Nirenberg inequality
• Sharp mutliplicative inequalities with BMO I
• New Bellman induction and a weak version of BMO
• The L^p-Operator Norm of a Quadratic Perturbation of the Real Part of\n the Ahlfors--Beurling Operator
• The John--Nirenberg constant of \rm BMO^p, p>2