Harmonic Analysis on Graphs: Maximal Bounds for Cartesian Powers of Finite Graphs
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چکیده
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
منابع مشابه
Dimensionally Exponential Lower Bounds on the $L^p$ Norms of the Spherical Maximal Operator for Cartesian Powers of Finite Trees and Related Graphs
Let T be a finite tree graph, TN be the Cartesian power graph of T , and dN be the graph distance metric on TN . Also let Sr (x) := {v ∈ T N : d (x, v) = r} be the sphere of radius r centered at x and M be the spherical maximal averaging operator on TN given by Mf(x) := sup r≥0 S N r (x) 6=∅ 1 |Sr (x)| ∣
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