an:01130498
Zbl 0892.43005
Franchi, Bruno; P??rez, Carlos; Wheeden, Richard L.
Self-improving properties of John-Nirenberg and Poincar?? inequalities on spaces of homogeneous type
EN
J. Funct. Anal. 153, No. 1, 108-146 (1998).
00047109
1998
j
43A85
self-improving properties of John-Nirenberg; Poincar?? inequalities; 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.
Bolis Basit (Clayton)