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

Authors :
Ghulam Murtaza
Toqeer Mahmood
Jia-Bao Liu
Zaryab Hussain
Source :
Mathematical Problems in Engineering, Vol 2021 (2021)
Publication Year :
2021
Publisher :
Hindawi Limited, 2021.

Abstract

Let G = G 1 × G 2 × ⋯ × G m 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 M G ϕ on ℓ p spaces. We determine the exact value of ℓ p -quasi-norm of M G ϕ for the case when G is strong product of complete graphs, where 0 < p ≤ 1 . However, lower and upper bounds of ℓ p -norm have been determined when 1 < p < ∞ . Finally, we computed the lower and upper bounds of M G ϕ p when G is strong product of arbitrary graphs, where 0 < p ≤ 1 .

Details

ISSN :
15635147 and 1024123X
Volume :
2021
Database :
OpenAIRE
Journal :
Mathematical Problems in Engineering
Accession number :
edsair.doi.dedup.....8149f14897492d39683ec57b88b836e2
Full Text :
https://doi.org/10.1155/2021/9338269