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2010 A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa
Tuomas Hytönen
Publ. Mat. 54(2): 485-504 (2010).

Abstract

A new class of metric measure spaces is introduced and studied. This class generalises the well-established doubling metric measure spaces as well as the spaces $(\mathbb{R}^n,\mu)$ with $\mu(B(x,r))\leq Cr^d$, in which non-doubling harmonic analysis has recently been developed. It seems to be a promising framework for an abstract extension of this theory. Tolsa's space of regularised BMO functions is defined in this new setting, and the John-Nirenberg inequality is proven.

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Tuomas Hytönen. "A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa." Publ. Mat. 54 (2) 485 - 504, 2010.

Information

Published: 2010
First available in Project Euclid: 28 June 2010

zbMATH: 1246.30087
MathSciNet: MR2675934

Subjects:
Primary: 30L99 , 42B35

Keywords: doubling balls , John-Nirenberg inequality , Non-doubling measure

Rights: Copyright © 2010 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.54 • No. 2 • 2010
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