Weak integral conditions for BMO

A. A. Logunov, L. Slavin, D. M. Stolyarov, V. Vasyunin, P. B. Zatitskiy

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We study the question of how much one can weaken the defining condition of BMO. Specifically, we show that if Q is a cube in Rn and h: [0,∞) → [0,∞) is such that h(t)→∞ as t→∞, then sup J subcube Q 1 |J|_ J h ϕ – 1 |J| J ϕ _< ∞ =⇒ ϕ ∈ BMO(Q). Under some additional assumptions on h we obtain estimates on _ϕ_BMO in terms of the supremum above. We also show that even though the limit condition on h is not necessary for this implication to hold, it becomes necessary if one considers the dyadic BMO.

Original languageEnglish (US)
Pages (from-to)2913-2926
Number of pages14
JournalProceedings of the American Mathematical Society
Volume143
Issue number7
DOIs
StatePublished - Jan 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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    Logunov, A. A., Slavin, L., Stolyarov, D. M., Vasyunin, V., & Zatitskiy, P. B. (2015). Weak integral conditions for BMO. Proceedings of the American Mathematical Society, 143(7), 2913-2926. https://doi.org/10.1090/S0002-9939-2015-12424-0