Banach Journal of Mathematical Analysis

An interpolation theorem for sublinear operators on non-homogeneous metric measure spaces

Haibo Lin and Dongyong Yang

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Abstract

Let $({\mathcal X}, d, \mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors establish an interpolation result that a sublinear operator which is bounded from the Hardy space $H^1(\mu)$ to $L^{1,\,\infty}(\mu)$ and from $L^\infty(\mu)$ to the BMO-type space RBMO($\mu$) is also bounded on $L^p(\mu)$ for all $p\in(1,\,\infty)$. This extension is not completely straightforward and improves the existing result

Article information

Source
Banach J. Math. Anal., Volume 6, Number 2 (2012), 168-179.

Dates
First available in Project Euclid: 13 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1342210167

Digital Object Identifier
doi:10.15352/bjma/1342210167

Mathematical Reviews number (MathSciNet)
MR2945995

Zentralblatt MATH identifier
1252.42025

Subjects
Primary: 42B35
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 47B38: Operators on function spaces (general)

Keywords
RBMO($\mu$)$ upper doubling geometrically doubling sublinear interpolation

Citation

Lin, Haibo; Yang, Dongyong. An interpolation theorem for sublinear operators on non-homogeneous metric measure spaces. Banach J. Math. Anal. 6 (2012), no. 2, 168--179. doi:10.15352/bjma/1342210167. https://projecteuclid.org/euclid.bjma/1342210167


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