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

Let be the strong product of simple, finite connected graphs, and let be an increasing function. We consider the action of generalized maximal operator on spaces. We determine the exact value of - quasi-norm of for the case when is strong product of complete graphs, where . However, lower and upper bounds of - norm have been determined when . Finally, we computed the lower and upper bounds of when is strong product of arbitrary graphs, where .