Sharp Inequalities for Maximal Operators on Finite Graphs

González-Riquelme, Cristian; Madrid, José

doi:10.1007/s12220-021-00625-0

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…For more details on this topic of research, see [4,8,[10][11][12][13]. e main motivation of this paper is from [4][5][6][7]10]. e paper is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

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

Hussain

Murtaza

Mahmood

et al. 2021

Mathematical Problems in Engineering

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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 .

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“…For more details on this topic of research, see [4,8,[10][11][12][13]. e main motivation of this paper is from [4][5][6][7]10]. e paper is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

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

Hussain

Murtaza

Mahmood

et al. 2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Over the last several years the Hardy-Littlewood maximal operator on graphs has been studied by many authors (see [10][11][12][13][14][15][16]). The Hardy-Littlewoood maximal operator on graphs was first introduced and studied by Korányi and Picardello [15] who used the above operator to explore the boundary behavior of eigenfunctions of the Laplace operator on trees.…”

Section: Introductionmentioning

confidence: 99%

“…Later, Soria and Tradacete [16] investigated some different geometric properties on infinite graphs, related to the weak-type boundedness of the Hardy-Littlewood maximal operator on infinite connected graphs. One can consult [13,14] for the variation properties of the Hardy-Littlewood maximal operator on finite connected graphs.…”

Section: Introductionmentioning

confidence: 99%