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$L^2$-Maximal functions on graded Lie groups by Cardona, Duván is a scholarly article available to read on EtoBox.

What is $L^2$-Maximal functions on graded Lie groups about?

Bourgain in his seminal paper [2] about the analysis of maximal functions associated to convex bodies, has estimated in a sharp way the $L^2$-operator norm of the maximal function associated to a kernel $K\in L^1,$ with differentiable Fourier transform $\widehat{K}.$ We formulate the extension to Bourgain's $L^2$-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.

Author

Cardona, Duván

Published

2024

Language

EN