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arXiv · 2405.16855

Maximal operators given by Fourier multipliers with dilation of fractional dimensions

Jin Bong Lee·Jinsol Seo
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Abstract

In this paper, we investigate $L^p$ bounds of maximal Fourier multiplier operators with dilation of fractional dimensions. For Fourier multipliers, we suggest a criterion related to dimensions of dilation sets which guarantees $L^p$ bounds of the maximal operators for each $p$. Our criterion covers Mikhlin-type multipliers, multipliers with limited decay, and multipliers with slow decay.

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Jin Bong Lee, Jinsol Seo. 2024-05-27. Maximal operators given by Fourier multipliers with dilation of fractional dimensions. https://arxiv.org/abs/2405.16855

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