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Harmonic Analysis on Graphs : Maximal Bounds for Cartesian Powers of Finite Graphs

My research in graph theory focuses on asymptotic maximal bounds for Cartesian powers of finite graphs. This line of inquiry was opened up by [4], in which the authors proved that the maximal spherical averaging operator on the N -dimensional hypercube K 2 satisfies a bound in the L 2 norm independent of the dimension N . That is, if Sk(x) := {y : d(x, y) = k} in the graph distance metric on K 2 , the L 2 norm of the function