Abstract
In this paper, we introduce and study the Hardy–Littlewood maximal operator MG→ on a finite directed graph G→. We obtain some optimal constants for the ℓp norm of MG→ by introducing two classes of directed graphs.
Highlights
The best constants for the Hardy–Littlewood maximal inequalities have always been a challenging topic of research
It should be pointed out that geometric structure of a graph plays an important role in studying maximal operators on graphs
Given the significance of this operator, it is an interesting and natural question to ask what happens when we consider the directed graphs. It is the purpose of this paper to investigate the optimal constants for thep norm of the
Summary
The best constants for the Hardy–Littlewood maximal inequalities have always been a challenging topic of research. Soria and Tradacete [10] studied the sharpp -norm for the Hardy-Littlewoood maximal operators on finite connected graphs. Given the significance of this operator, it is an interesting and natural question to ask what happens when we consider the directed graphs It is the purpose of this paper to investigate the optimal constants for thep norm of the. Hardy–Littlewood maximal operator in directed graph setting. Soria and Tradacete [10] studied the best constants for thep -norm of the Hardy-Littlewoood maximal operators on finite connected graphs. 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. Hardy–Littlewood maximal operator on finite connected graphs.
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