Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs

Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs

Let G=G1×G2×⋯×Gm be the strong product of simple, finite connected graphs, and let ϕ:ℕ⟶0,∞ be an increasing function. We consider the action of generalized maximal operator MGϕ on ℓp spaces. We determine the exact value of ℓp-quasi-norm of MGϕ for the case when G is strong product of complete graphs...

Full description

Bibliographic Details
Main Authors: Zaryab Hussain, Ghulam Murtaza, Toqeer Mahmood, Jia-Bao Liu
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2021/9338269
id doaj-6a94e78260854baf9b5042e4958591b4
record_format Article
spelling doaj-6a94e78260854baf9b5042e4958591b42021-07-19T01:05:09ZengHindawi LimitedMathematical Problems in Engineering1563-51472021-01-01202110.1155/2021/9338269Estimates for the Norm of Generalized Maximal Operator on Strong Product of GraphsZaryab Hussain0Ghulam Murtaza1Toqeer Mahmood2Jia-Bao Liu3School of Mathematics and StatisticsDepartment of MathematicsDepartment of Computer ScienceSchool of Mathematics and PhysicsLet G=G1×G2×⋯×Gm be the strong product of simple, finite connected graphs, and let ϕ:ℕ⟶0,∞ be an increasing function. We consider the action of generalized maximal operator MGϕ on ℓp spaces. We determine the exact value of ℓp-quasi-norm of MGϕ for the case when G is strong product of complete graphs, where 0<p≤1. However, lower and upper bounds of ℓp-norm have been determined when 1<p<∞. Finally, we computed the lower and upper bounds of MGϕp when G is strong product of arbitrary graphs, where 0<p≤1.http://dx.doi.org/10.1155/2021/9338269
collection DOAJ
language English
format Article
sources DOAJ
author Zaryab Hussain
Ghulam Murtaza
Toqeer Mahmood
Jia-Bao Liu
spellingShingle Zaryab Hussain
Ghulam Murtaza
Toqeer Mahmood
Jia-Bao Liu
Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs
Mathematical Problems in Engineering
author_facet Zaryab Hussain
Ghulam Murtaza
Toqeer Mahmood
Jia-Bao Liu
author_sort Zaryab Hussain
title Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs
title_short Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs
title_full Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs
title_fullStr Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs
title_full_unstemmed Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs
title_sort estimates for the norm of generalized maximal operator on strong product of graphs
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1563-5147
publishDate 2021-01-01
description Let G=G1×G2×⋯×Gm be the strong product of simple, finite connected graphs, and let ϕ:ℕ⟶0,∞ be an increasing function. We consider the action of generalized maximal operator MGϕ on ℓp spaces. We determine the exact value of ℓp-quasi-norm of MGϕ for the case when G is strong product of complete graphs, where 0<p≤1. However, lower and upper bounds of ℓp-norm have been determined when 1<p<∞. Finally, we computed the lower and upper bounds of MGϕp when G is strong product of arbitrary graphs, where 0<p≤1.
url http://dx.doi.org/10.1155/2021/9338269
work_keys_str_mv AT zaryabhussain estimatesforthenormofgeneralizedmaximaloperatoronstrongproductofgraphs
AT ghulammurtaza estimatesforthenormofgeneralizedmaximaloperatoronstrongproductofgraphs
AT toqeermahmood estimatesforthenormofgeneralizedmaximaloperatoronstrongproductofgraphs
AT jiabaoliu estimatesforthenormofgeneralizedmaximaloperatoronstrongproductofgraphs
_version_ 1721295437384646656

Similar Items