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Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous type. (English) Zbl 0892.43005
The authors consider inequalities of the form \[ \underset{\mu(B)}\bot \int_B| f-f_B| d\mu\leq ca(B)\quad\text{and} \quad \underset{\mu(B)}\bot \int_B | f-f_B| d\mu\leq cb(B,f). \] 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.

MSC:
43A85 Harmonic analysis on homogeneous spaces
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