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Zbl 0892.43005
Franchi, Bruno; Pérez, Carlos; Wheeden, Richard L.
Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous type. (English)
[J] J. Funct. Anal. 153, No.1, 108-146 (1998). ISSN 0022-1236

The authors consider inequalities of the form $$\underset{\mu(B)}\to\bot \int_B| f-f_B| d\mu\le ca(B)\quad\text{and} \quad \underset{\mu(B)}\to\bot \int_B | f-f_B| d\mu\le cb(B,f).$$ In either case $\mu$ is a measure and $\mu(B)$ denotes the $\mu$-measure of $B$. The main goal of this paper is to show that under certain conditions of geometric type on the functionals $a$ and $b$ both inequalities encode an intrinsic $L^r$ self-improving property.
[Bolis Basit (Clayton)]

MSC 2000:: *43A85 Analysis on homogeneous spaces

Keywords: self-improving properties of John-Nirenberg; Poincaré inequalities; spaces of homogeneous type

Cited in: Zbl 1172.46020 Zbl 1101.42010 Zbl 1074.46022 Zbl 0931.26007

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