# Quantitative John-Nirenberg inequalities at different scales

@article{MartinezPerales2020QuantitativeJI, title={Quantitative John-Nirenberg inequalities at different scales}, author={Javier C. Mart'inez-Perales and Ezequiel Rela and Israel P. Rivera-R'ios}, journal={arXiv: Classical Analysis and ODEs}, year={2020} }

We provide an abstract estimate of the form \[
\|f-f_{Q,\mu}\|_{X \left(Q,\frac{\mathrm{d} \mu}{Y(Q)}\right)}\leq c(\mu,Y)\psi(X)\|f\|_{\mathrm{BMO}(\mathrm{d}\mu)} \] for all cubes $Q$ in $\mathbb{R}^n$ and every function $f\in \mathrm{BMO}(\mathrm{d}\mu)$, where $\mu$ is a doubling measure in $\mathbb{R}^n$, $Y$ is some positive functional defined on cubes, $\|\cdot \|_{X \left(Q,\frac{\mathrm{d} w}{w(Q)}\right)}$ is a sufficiently good quasi-norm and $c(\mu,Y)$ and $\psi(X)$ are positive…

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