BMO and the John-Nirenberg Inequality on Measure Spaces-Reference-Cited by-同舟云学术

BMO and the John-Nirenberg Inequality on Measure Spaces

Published:2020-01-01 Issue:1 Volume:8 Page:335-362
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:en
Short-container-title:

Author:

Dafni Galia¹,Gibara Ryan²,Lavigne Andrew³

Affiliation:

1. Concordia University , Montréal , Canada

2. Université Laval , Département de mathématiques et de statistique , Québec , QC G1V 0A6 , Canada

3. McGill University , Montréal , Canada

Abstract

Abstract We study the space BMO𝒢 (𝕏) in the general setting of a measure space 𝕏 with a fixed collection 𝒢 of measurable sets of positive and finite measure, consisting of functions of bounded mean oscillation on sets in 𝒢. The aim is to see how much of the familiar BMO machinery holds when metric notions have been replaced by measure-theoretic ones. In particular, three aspects of BMO are considered: its properties as a Banach space, its relation with Muckenhoupt weights, and the John-Nirenberg inequality. We give necessary and sufficient conditions on a decomposable measure space 𝕏 for BMO𝒢 (𝕏) to be a Banach space modulo constants. We also develop the notion of a Denjoy family 𝒢, which guarantees that functions in BMO𝒢 (𝕏) satisfy the John-Nirenberg inequality on the elements of 𝒢.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2020-0115/pdf

Reference27 articles.

1. [1] Brezis, H.; Nirenberg, L. Degree theory and BMO. I. Compact manifolds without boundaries. Selecta Math. (N.S.) 1 (1995), no. 2, 197-263.

2. [2] Buckley, S. M. Inequalities of John-Nirenberg type in doubling spaces. J. Anal. Math. 79 (1999), 215-240.

3. [3] Chen, Y. Z.; Lau, K.-S. Some new classes of Hardy spaces. J. Funct. Anal. 84 (1989), no. 2, 255-278.

4. [4] Coifman, R. R.; Weiss, G. Analyse harmonique non-commutative sur certains espaces homogènes. (French) Étude de certaines intégrales singulières. Lecture Notes in Mathematics, Vol. 242. Springer-Verlag, Berlin-New York, 1971. v+160 pp.

5. [5] Coifman, R. R.; Weiss, G. Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83 (1977), no. 4, 569-645.

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