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Maysami Sadr, Maysam. (1403). A modification of Hardy-Littlewood maximal-function on Lie groups. نشریه مهندسی عمران امیرکبیر, 5(2), 143-149. doi: 10.22060/ajmc.2023.22259.1147
Maysam Maysami Sadr. "A modification of Hardy-Littlewood maximal-function on Lie groups". نشریه مهندسی عمران امیرکبیر, 5, 2, 1403, 143-149. doi: 10.22060/ajmc.2023.22259.1147
Maysami Sadr, Maysam. (1403). 'A modification of Hardy-Littlewood maximal-function on Lie groups', نشریه مهندسی عمران امیرکبیر, 5(2), pp. 143-149. doi: 10.22060/ajmc.2023.22259.1147
Maysami Sadr, Maysam. A modification of Hardy-Littlewood maximal-function on Lie groups. نشریه مهندسی عمران امیرکبیر, 1403; 5(2): 143-149. doi: 10.22060/ajmc.2023.22259.1147

A modification of Hardy-Littlewood maximal-function on Lie groups

AUT Journal of Mathematics and Computing
مقاله 6، دوره 5، شماره 2، 2024، صفحه 143-149    اصل مقاله (416.39 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22259.1147
نویسنده
Maysam Maysami Sadr*
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran
چکیده
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.
کلیدواژه‌ها
Hardy-Littlewood maximalfunction؛ Lie group؛ Metric measure space؛ Boundedness of sublinear؛ operators
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