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## A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”

#### Zaryab HUSSAİN [1] , Sadia TALİB [2]

Let $G{m}_{n}$ be a simple, connected and finite graph. Suppose $\phi: \mathbb{N}\to \mathbb{R^{+}}$ is a positive and increasing function. We consider the action of generalized maximal operator $M^{\phi}_{G^{m}_{n}}$ on $\ell^{p}$ spaces and find optimal bound for the quasi norm $\|M^{\phi}_{G^{m}_{n}}\|_{p}$ for the case $0<p\leq 1$. In addition we find bounds for the norm $\|M^{\phi}_{G^{m}_{n}}\|_{p}$ for the case $1<p<\infty$. We also prove some general results for $0<p\leq 1$.
generalized maximal operator, $\ell^{p}$-estimates, $G^{m}_{n}$ graph
• [1] I. Ahmad and W. Nazeer, Optimal Couples of Rearrangement Invariant Spaces for Generalized Maximal Operators, J. Funct. Spaces 2014, Article ID 647123, 5 pages, 2014.
• [2] J. Soria and P. Tradacete, Best constants for the Hardy-Littlewood maximal operator on finite graphs, J. Math. Anal. Appl. 436 (2), 661–682, 2016.
Birincil Dil en Matematik Matematik Orcid: 0000-0002-9218-7735Yazar: Zaryab HUSSAİN (Sorumlu Yazar)Kurum: University of Central PunjabÜlke: Pakistan Orcid: 0000-0002-9388-9122Yazar: Sadia TALİB Kurum: Government College UniversityÜlke: Pakistan Yayımlanma Tarihi : 2 Nisan 2020
 Bibtex @araştırma makalesi { hujms471101, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {498 - 504}, doi = {10.15672/hujms.471101}, title = {A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”}, key = {cite}, author = {HUSSAİN, Zaryab and TALİB, Sadia} } APA HUSSAİN, Z , TALİB, S . (2020). A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 498-504 . DOI: 10.15672/hujms.471101 MLA HUSSAİN, Z , TALİB, S . "A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 498-504 Chicago HUSSAİN, Z , TALİB, S . "A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 498-504 RIS TY - JOUR T1 - A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs” AU - Zaryab HUSSAİN , Sadia TALİB Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.471101 DO - 10.15672/hujms.471101 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 498 EP - 504 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.471101 UR - https://doi.org/10.15672/hujms.471101 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs” %A Zaryab HUSSAİN , Sadia TALİB %T A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs” %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.471101 %U 10.15672/hujms.471101 ISNAD HUSSAİN, Zaryab , TALİB, Sadia . "A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 498-504 . https://doi.org/10.15672/hujms.471101 AMA HUSSAİN Z , TALİB S . A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 498-504. Vancouver HUSSAİN Z , TALİB S . A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 504-498.

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