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arXiv · 2508.00279

Estimates for maximal Fourier multiplier operators on $\Bbb R^2$ via square functions

Shuichi Sato
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Abstract

We consider certain Littlewood-Paley square functions on $\Bbb R^2$ and prove sharp estimates for them, from which we can deduce $L^p$ boundedness of maximal functions defined by Fourier multipliers of Bochner-Riesz type on $\Bbb R^2$. This is a generalization of a result due to A. Carbery 1983.

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Shuichi Sato. 2025-08-01. Estimates for maximal Fourier multiplier operators on $\Bbb R^2$ via square functions. https://arxiv.org/abs/2508.00279

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