Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous type
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.
self-improving properties of John-Nirenberg
scientific article; zbMATH DE number 1130498
scientific article