@article {
author = {Maysami Sadr, Maysam},
title = {A modification of Hardy-Littlewood maximal-function on Lie groups},
journal = {AUT Journal of Mathematics and Computing},
volume = {5},
number = {2},
pages = {143-149},
year = {2024},
publisher = {Amirkabir University of Technology},
issn = {2783-2449},
eissn = {2783-2287},
doi = {10.22060/ajmc.2023.22259.1147},
abstract = {For a real-valued function $f$ on a metric measure space $(X,d,\mu)$ the Hardy-Littlewood centered-ball maximal-function of $f$ is given by the `supremum-norm':$$Mf(x):=\sup_{r>0}\frac{1}{\mu(\mathcal{B}_{x,r})}\int_{\mathcal{B}_{x,r}}|f|d\mu.$$In this note, we replace the supremum-norm on parameters $r$ by $\mathcal{L}_p$-norm with weight $w$ on parameters $r$ and define Hardy-Littlewood integral-function $I_{p,w}f$. It is shown that $I_{p,w}f$ converges pointwise to $Mf$ as $p\to\infty$. Boundedness of the sublinear operator $I_{p,w}$ and continuity of the function $I_{p,w}f$ in case that $X$ is a Lie group, $d$ is a left-invariant metric, and $\mu$ is a left Haar-measure (resp. right Haar-measure) are studied.},
keywords = {Hardy-Littlewood maximalfunction,Lie group,metric measure space,Boundedness of sublinear,operators},
url = {https://ajmc.aut.ac.ir/article_5157.html},
eprint = {https://ajmc.aut.ac.ir/article_5157_baa11da9a85053a25ed30948c0b7ae4c.pdf}
}