Research Article
BibTex RIS Cite
Year 2020, Volume: 49 Issue: 2, 498 - 504, 02.04.2020
https://doi.org/10.15672/hujms.471101

Abstract

References

  • [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.

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

Year 2020, Volume: 49 Issue: 2, 498 - 504, 02.04.2020
https://doi.org/10.15672/hujms.471101

Abstract

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 $0<p\leq 1$.

References

  • [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.
There are 2 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Zaryab Hussain 0000-0002-9218-7735

Sadia Talib 0000-0002-9388-9122

Publication Date April 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 2

Cite

APA Hussain, Z., & Talib, 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. https://doi.org/10.15672/hujms.471101
AMA Hussain Z, Talib S.A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs.” Hacettepe Journal of Mathematics and Statistics. April 2020;49(2):498-504. doi:10.15672/hujms.471101
Chicago Hussain, Zaryab, and Sadia Talib. “A Note on the Paper ‘Best Constants for the Hardy−Litllewood Maximal Operator on Finite graphs’”. Hacettepe Journal of Mathematics and Statistics 49, no. 2 (April 2020): 498-504. https://doi.org/10.15672/hujms.471101.
EndNote Hussain Z, Talib S (April 1, 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.
IEEE Z. Hussain and S. Talib, “A note on the paper ‘Best constants for the Hardy−Litllewood maximal operator on finite graphs’”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, pp. 498–504, 2020, doi: 10.15672/hujms.471101.
ISNAD Hussain, Zaryab - Talib, 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 (April 2020), 498-504. https://doi.org/10.15672/hujms.471101.
JAMA Hussain Z, Talib S. A note on the paper “Best constants for the Hardy−Litllewood maximal operator on finite graphs”. Hacettepe Journal of Mathematics and Statistics. 2020;49:498–504.
MLA Hussain, Zaryab and Sadia Talib. “A Note on the Paper ‘Best Constants for the Hardy−Litllewood Maximal Operator on Finite graphs’”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, 2020, pp. 498-04, doi:10.15672/hujms.471101.
Vancouver Hussain Z, Talib 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.