Sharp mutliplicative inequalities with BMO I

2020/01/26 by Dmitriy Stolyarov, Stolyarov, Dmitriy, Vasily Vasyunin +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2001.09454

openalex publication_date 2020/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find the best possible constant C in the inequality ‖φ‖Lr≤ C‖φ‖Lp(p)/(r)‖φ‖BMO1-(p)/(r), where 2 ≤ r and p < 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.

Related

• Sharp results in the integral-form John--Nirenberg inequality
• Sharp L^p estimates on BMO
• Sharp transference principle for BMO and A_p
• The John--Nirenberg constant of \rm BMO^p, 1≤ p≤ 2
• A Gagliardo-Nirenberg type inequality for rapidly decaying functions