6533b7d8fe1ef96bd1269b9f

RESEARCH PRODUCT

Finitely randomized dyadic systems and BMO on metric measure spaces

Toni HeikkinenJanne Korvenpää

subject

Discrete mathematicsMathematics::Functional AnalysisDyadic cubeApplied Mathematicsta111Mathematics::Analysis of PDEsMathematics::Classical Analysis and ODEsMetric measure spaceBounded mean oscillationQuantitative Biology::OtherBounded mean oscillationRandomized dyadic systemMetric spaceNorm (mathematics)Dyadic BMOAnalysisMathematics

description

Abstract We study the connection between BMO and dyadic BMO in metric measure spaces using finitely randomized dyadic systems, and give a Garnett–Jones type proof for a theorem of Uchiyama on a construction of certain BMO functions. We obtain a relation between the BMO norm of a suitable expectation over dyadic systems and the dyadic BMO norms of the original functions in different systems. The expectation is taken over only finitely randomized dyadic systems to overcome certain measurability questions. Applying our result, we derive Uchiyama’s theorem from its dyadic counterpart, which we also prove.

yearjournalcountryeditionlanguage
2015-06-01Nonlinear Analysis: Theory, Methods & Applications
https://doi.org/10.1016/j.na.2015.02.015