John-Nirenberg lemmas for a doubling measure

Abstract

We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.

arXiv comment17 pages, some typos corrected

Cited by in corpus (16)

• The space $J{N}_p$: nontriviality and duality
• Aspects of local to global results
• Oscillation estimates, self-improving results and good-$\lambda$ inequalities
• A Survey on Function Spaces of John--Nirenberg Type
• Nontrivial examples of $J{N}_p$ and $VJ{N}_p$ functions
• New John--Nirenberg--Campanato-Type Spaces Related to Both Maximal Functions and Their Commutators
• BMO on shapes and sharp constants
• The John-Nirenberg space: Equality of the vanishing subspaces $VJ{N}_p$ and $CJ{N}_p$
• Two Phase Free Boundary Problem for Poisson Kernels
• Dyadic John-Nirenberg space
• John--Nirenberg--Campanato Spaces
• Median-type John-Nirenberg space in metric measure spaces
• Parabolic John-Nirenberg spaces
• Boundedness of Calderón--Zygmund Operators on Special John--Nirenberg--Campanato and Hardy-Type Spaces via Congruent Cubes
• The Capacitary John-Nirenberg Inequality Revisited
• Localized John--Nirenberg--Campanato Spaces