L²-Maximal functions on graded Lie groups

2024/01/19 by Cardona, Duván
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2401.10830

Abstract

Bourgain in his seminal paper [2] about the analysis of maximal functions associated to convex bodies, has estimated in a sharp way the L²-operator norm of the maximal function associated to a kernel K∈ L¹, with differentiable Fourier transform \widehatK. We formulate the extension to Bourgain's L²-estimate in the setting of maximal functions on graded Lie groups. Our criterion is formulated in terms of the group Fourier transform of the kernel. We discuss the application of our main result to the L^p-boundedness of maximal functions on graded Lie groups.

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