John–Nirenberg Inequalities and Weight Invariant BMO Spaces

This work explores new deep connections between John–Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BMO -type spaces. The results are formulated in a very general framework in which BMO spaces are constructed using a base of sets, used also to define weights with...

Full description

Saved in:
Bibliographic Details
Published inThe Journal of geometric analysis Vol. 29; no. 2; pp. 1608 - 1648
Main Authors Hart, Jarod, Torres, Rodolfo H.
Format Journal Article
LanguageEnglish
Published New York Springer US 15.04.2019
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Function space
Geometry
Global Analysis and Analysis on Manifolds
Inequalities
Invariance
Mathematics
Mathematics and Statistics
Weight
Weight invariance
Spaces of bounded mean oscillations
John–Nirenberg inequality
BMO
Muckenhoupt weights
Online AccessGet full text

Cover

More Information
Summary:This work explores new deep connections between John–Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BMO -type spaces. The results are formulated in a very general framework in which BMO spaces are constructed using a base of sets, used also to define weights with respect to a non-negative measure (not necessarily doubling), and an appropriate oscillation functional. This includes as particular cases many different function spaces on geometric settings of interest. As a consequence, the weight invariance of several BMO and Triebel–Lizorkin spaces considered in the literature is proved. Most of the invariance results obtained under this unifying approach are new even in the most classical settings.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-018-0054-y